 2.2.7.1: A curve has equation . (a) Write an expression for the slope of the...
 2.2.3.1: Given that lim t!x" ! "2 xl 2 f!x" ! 4 lim h!x" ! 0 xl 2 lim t!x" !...
 2.2.8.1: (a) How is the number e defined? (b) Use a calculator to estimate t...
 2.2.4.1: Use the given graph of f"x# ! 1&x to find a number suchthat if x ! ...
 2.2.5.1: Write an equation that expresses the fact that a function is contin...
 2.2.6.1: Explain in your own words the meaning of each of the f !x" followin...
 2.2.1.2: A tank holds 1000 gallons of water, which drains from the bottom of...
 2.2.2.1: Explain in your own words what is meant by the equation Is it possi...
 2.2.7.2: Graph the curve in the viewing rectangles by , by , and by . What d...
 2.2.3.2: The graphs of and t are given. Use them to evaluate each limit, if ...
 2.2.8.2: Use the given graph to estimate the value of each derivative. fThen...
 2.2.4.2: Use the given graph of to find a number such that if 0 " ! x ! 5 ! ...
 2.2.5.2: If f is continuous on , what can you say about its graph?
 2.2.6.2: (a) Can the graph of y ! f !xintersect a vertical asymptote? Can it...
 2.2.1.3: A cardiac monitor is used to measure the heart rate of a patient af...
 2.2.2.2: Explain what it means to say that and In this situation is it possi...
 2.2.7.3: (a) Find the slope of the tangent line to the parabola at the point...
 2.2.3.3: Evaluate the limit and justify each step by indicating the appropri...
 2.2.8.3: Match the graph of each function in (a)(d) with the graph of its de...
 2.2.4.3: Use the given graph of to find a number such that if x ! 4 ! " # th...
 2.2.5.3: (a) From the graph of , state the numbers at which is discontinuous...
 2.2.6.3: For the function whose graph is given, state the following.
 2.2.1.4: The point lies on the curve . (a) If is the point , use your calcul...
 2.2.2.3: Explain the meaning of each of the following
 2.2.7.4: (a) Find the slope of the tangent line to the curve at the point (i...
 2.2.3.4: Evaluate the limit and justify each step by indicating the appropri...
 2.2.8.4: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.4: Use the given graph of to find a number such that if then ! x 2 ! 1...
 2.2.5.4: From the graph of , state the intervals on which is continuous.
 2.2.6.4: For the function whose graph is given, state the following.
 2.2.1.5: The point lies on the curve . (a) If is the point , use your calcul...
 2.2.2.4: For the function whose graph is given, state the value of each quan...
 2.2.7.5: Find an equation of the tangent line to the curve at the given point.
 2.2.3.5: Evaluate the limit and justify each step by indicating the appropri...
 2.2.8.5: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.5: Use a graph to find a number # such that if x ! tan x ! 1! " 0.2 *4...
 2.2.5.5: Sketch the graph of a function that is continuous everywhere except...
 2.2.6.5: Sketch the graph of an example of a function that satisfies all of ...
 2.2.1.6: If a ball is thrown into the air with a velocity of 40 ft#s, its he...
 2.2.2.5: Use the given graph of to state the value of each quantity, if it e...
 2.2.2.6: For the function whose graph is given, state the value of each quan...
 2.2.7.6: Find an equation of the tangent line to the curve at the given point.
 2.2.3.6: Evaluate the limit and justify each step by indicating the appropri...
 2.2.8.6: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.6: Use a graph to find a number such that if x ! 1! " # then x 2 & 4 !...
 2.2.5.6: Sketch the graph of a function that has a jump discontinuity at and...
 2.2.6.6: Sketch the graph of an example of a function that satisfies all of ...
 2.2.1.7: If a rock is thrown upward on the planet Mars with a velocity of 10...
 2.2.2.7: For the function whose graph is given, state the value of each quan...
 2.2.7.7: Find an equation of the tangent line to the curve at the given point.
 2.2.3.7: Evaluate the limit and justify each step by indicating the appropri...
 2.2.8.7: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.7: For the limit limxl0e x ! 1x ! 1
 2.2.5.7: A parking lot charges $3 for the first hour (or part of an hour) an...
 2.2.6.7: Sketch the graph of an example of a function that satisfies all of ...
 2.2.1.8: The table shows the position of a cyclist. (a) Find the average vel...
 2.2.2.8: For the function whose graph is shown, state the following.
 2.2.7.8: Find an equation of the tangent line to the curve at the given point.
 2.2.3.8: Evaluate the limit and justify each step by indicating the appropri...
 2.2.8.8: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.8: For the limit limxl0e x ! 1x ! 1 illustrate Definition 2 by finding...
 2.2.5.8: Explain why each function is continuous or discontinuous. (a) The t...
 2.2.6.8: Sketch the graph of an example of a function that satisfies all of ...
 2.2.1.9: The displacement (in centimeters) of a particle moving back and for...
 2.2.2.9: . For the function whose graph is shown, state the following.
 2.2.7.9: (a) Find the slope of the tangent to the curve at the point where ....
 2.2.3.9: Evaluate the limit and justify each step by indicating the appropri...
 2.2.8.9: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.9: Given that limxl*&2 tan2x ! ( illustrate Definition 6 byfinding val...
 2.2.5.9: If and are continuous functions with f !3" ! 5 and limx l 3 $2 f !x...
 2.2.6.9: Sketch the graph of an example of a function that satisfies all of ...
 2.2.1.10: The point lies on the curve . (a) If is the point , find the slope ...
 2.2.2.10: A patient receives a 150mg injection of a drug every 4 hours. The ...
 2.2.7.10: (a) Find the slope of the tangent to the curve at the point where ....
 2.2.3.10: (a) What is wrong with the following equation? (b) In view of part ...
 2.2.8.10: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.10: Use a graph to find a number # such that if 5 " x " 5 & # then sx !...
 2.2.5.10: Use the definition of continuity and the properties of limits to sh...
 2.2.6.10: Sketch the graph of an example of a function that satisfies all of ...
 2.2.2.11: Use the graph of the function f!x" ! 1&!1 ! e1&x 11. " to state the...
 2.2.7.11: (a) A particle starts by moving to the right along a horizontal lin...
 2.2.3.11: Evaluate the limit, if it exists
 2.2.8.11: Trace or copy the graph of the given function . (Assume that the ax...
 2.2.4.11: A machinist is required to manufacture a circular metal disk with a...
 2.2.5.11: Use the definition of continuity and the properties of limits to sh...
 2.2.6.11: Guess the value of the limit limxl"x 22x by evaluating the function...
 2.2.2.12: Sketch the graph of the following function and use it to determine ...
 2.2.7.12: Shown are graphs of the position functions of two runners, and , wh...
 2.2.3.12: Evaluate the limit, if it exists
 2.2.8.12: Shown is the graph of the population function for yeast cells in a ...
 2.2.4.12: A crystal growth furnace is used in research to determine how best ...
 2.2.5.12: Use the definition of continuity and the properties of limits to sh...
 2.2.6.12: Use a graph of f!x" ! &1 ! 2x 'x estimate the value of correct to t...
 2.2.2.13: Sketch the graph of an example of a function that satisfies all of ...
 2.2.7.13: If a ball is thrown into the air with a velocity of 40 ft!s, its he...
 2.2.3.13: Evaluate the limit, if it exists
 2.2.8.13: The graph shows how the average age of first marriage of Japanese m...
 2.2.4.13: (a) Find a number such that if b) Repeat part (a) with $ ! 0.01
 2.2.5.13: Use the definition of continuity and the properties of limits to sh...
 2.2.6.13: Evaluate the limit and justify each step by indicating the appropri...
 2.2.2.14: Sketch the graph of an example of a function that satisfies all of ...
 2.2.7.14: If a rock is thrown upward on the planet Mars with a velocity of , ...
 2.2.3.14: Evaluate the limit, if it exists
 2.2.8.14: Make a careful sketch of the graph of and below it sketch the graph...
 2.2.4.14: Given that limxl2 "5x ! 7# ! 3 illustrate Definition 2 byfinding va...
 2.2.5.14: Use the definition of continuity and the properties of limits to sh...
 2.2.6.14: Evaluate the limit and justify each step by indicating the appropri...
 2.2.2.15: Sketch the graph of an example of a function that satisfies all of ...
 2.2.7.15: The displacement (in meters) of a particle moving in a straight lin...
 2.2.3.15: Evaluate the limit, if it exists
 2.2.8.15: Make a careful sketch of the graph of and below it sketch the graph...
 2.2.4.15: Prove the statement using the definition of limit and illustrate wi...
 2.2.5.15: Explain why the function is discontinuous at the given number . Ske...
 2.2.6.15: Find the limit
 2.2.2.16: Sketch the graph of an example of a function that satisfies all of ...
 2.2.7.16: The displacement (in meters) of a particle moving in a straight lin...
 2.2.3.16: Evaluate the limit, if it exists
 2.2.8.16: Make a careful sketch of the graph of and below it sketch the graph...
 2.2.4.16: Prove the statement using the definition of limit and illustrate wi...
 2.2.5.16: Explain why the function is discontinuous at the given number . Ske...
 2.2.6.16: Find the limit
 2.2.2.17: Guess the value of the limit (if it exists) by evaluating the funct...
 2.2.7.17: For the function t whose graph is given, arrange the following numb...
 2.2.3.17: Evaluate the limit, if it exists
 2.2.8.17: Let f !x" ! x 2, , , and by using a graphing device to zoom in on t...
 2.2.4.17: Prove the statement using the definition of limit and illustrate wi...
 2.2.5.17: Explain why the function is discontinuous at the given number . Ske...
 2.2.6.17: Find the limit
 2.2.2.18: Guess the value of the limit (if it exists) by evaluating the funct...
 2.2.7.18: (a) Find an equation of the tangent line to the graph of at if and ...
 2.2.3.18: Evaluate the limit, if it exists
 2.2.8.18: Let f!x" ! x 3(a) Estimate the values of , , , , and by using a gra...
 2.2.4.18: Prove the statement using the definition of limit and illustrate wi...
 2.2.5.18: Explain why the function is discontinuous at the given number . Ske...
 2.2.6.18: Find the limit
 2.2.2.19: Guess the value of the limit (if it exists) by evaluating the funct...
 2.2.7.19: Sketch the graph of a function for which , , and
 2.2.3.19: Evaluate the limit, if it exists
 2.2.8.19: Find the derivative of the function using the definition of derivat...
 2.2.4.19: Prove the statement using the $, # definition of limit.
 2.2.5.19: Explain why the function is discontinuous at the given number . Ske...
 2.2.6.19: Find the limit
 2.2.2.20: Guess the value of the limit (if it exists) by evaluating the funct...
 2.2.7.20: Sketch the graph of a function for which , , and
 2.2.3.20: Evaluate the limit, if it exists
 2.2.8.20: Find the derivative of the function using the definition of derivat...
 2.2.4.20: Prove the statement using the $, # definition of limit.
 2.2.5.20: Explain why the function is discontinuous at the given number . Ske...
 2.2.6.20: Find the limit
 2.2.2.21: Use a table of values to estimate the value of the limit. If you ha...
 2.2.7.21: If , find and use it to find an equation of the tangent line to the...
 2.2.3.21: Evaluate the limit, if it exists
 2.2.8.21: Find the derivative of the function using the definition of derivat...
 2.2.4.21: Prove the statement using the $, # definition of limit.
 2.2.5.21: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.21: Find the limit
 2.2.2.22: Use a table of values to estimate the value of the limit. If you ha...
 2.2.7.22: If , find and use it to find an equation of the tangent line to the...
 2.2.3.22: Evaluate the limit, if it exists
 2.2.8.22: Find the derivative of the function using the definition of derivat...
 2.2.4.22: Prove the statement using the $, # definition of limit.
 2.2.5.22: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.22: Find the limit
 2.2.2.23: Use a table of values to estimate the value of the limit. If you ha...
 2.2.7.23: (a) If , find and use it to find an equation of the tangent line to...
 2.2.3.23: Evaluate the limit, if it exists
 2.2.8.23: Find the derivative of the function using the definition of derivat...
 2.2.4.23: Prove the statement using the $, # definition of limit.
 2.2.5.23: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.23: Find the limit
 2.2.2.24: Use a table of values to estimate the value of the limit. If you ha...
 2.2.7.24: (a) If , find and use it to find equations of the tangent lines to ...
 2.2.3.24: Evaluate the limit, if it exists
 2.2.8.24: Find the derivative of the function using the definition of derivat...
 2.2.4.24: Prove the statement using the $, # definition of limit.
 2.2.5.24: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.24: Find the limit
 2.2.2.25: Determine the infinite limit
 2.2.7.25: Find f )"a#
 2.2.3.25: Evaluate the limit, if it exists
 2.2.8.25: Find the derivative of the function using the definition of derivat...
 2.2.4.25: Prove the statement using the $, # definition of limit.
 2.2.5.25: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.25: Find the limit
 2.2.2.26: Determine the infinite limit
 2.2.7.26: Find f )"a#
 2.2.3.26: Evaluate the limit, if it exists
 2.2.8.26: Find the derivative of the function using the definition of derivat...
 2.2.4.26: Prove the statement using the $, # definition of limit.
 2.2.5.26: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.26: Find the limit
 2.2.2.27: Determine the infinite limit
 2.2.7.27: Find f )"a#
 2.2.3.27: Evaluate the limit, if it exists
 2.2.8.27: Find the derivative of the function using the definition of derivat...
 2.2.4.27: Prove the statement using the $, # definition of limit.
 2.2.5.27: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.27: Find the limit
 2.2.2.28: Determine the infinite limit
 2.2.7.28: Find f )"a#
 2.2.3.28: Evaluate the limit, if it exists
 2.2.8.28: Find the derivative of the function using the definition of derivat...
 2.2.4.28: Prove the statement using the $, # definition of limit.
 2.2.5.28: Explain, using Theorems 4, 5, 7, and 9, why the function is continu...
 2.2.6.28: Find the limit
 2.2.2.29: Determine the infinite limit
 2.2.7.29: Find f )"a#
 2.2.3.29: Evaluate the limit, if it exists
 2.2.8.29: Find the derivative of the function using the definition of derivat...
 2.2.4.29: Prove the statement using the $, # definition of limit.
 2.2.5.29: Locate the discontinuities of the function and illustrate by graphi...
 2.2.6.29: Find the limit
 2.2.2.30: Determine the infinite limit
 2.2.7.30: Find f )"a#
 2.2.3.30: Evaluate the limit, if it exists
 2.2.8.30: (a) Sketch the graph of by starting with the graph of and using the...
 2.2.4.30: Prove the statement using the $, # definition of limit.
 2.2.5.30: Locate the discontinuities of the function and illustrate by graphi...
 2.2.6.30: Find the limit
 2.2.2.31: Determine the infinite limit
 2.2.7.31: Each limit represents the derivative of some function at some numbe...
 2.2.3.31: (a) Estimate the value of by graphing the function . (b) Make a tab...
 2.2.8.31: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 2.2.4.31: Prove the statement using the $, # definition of limit.
 2.2.5.31: Use continuity to evaluate the limit
 2.2.6.31: Find the limit
 2.2.2.32: Determine the infinite limit
 2.2.7.32: Each limit represents the derivative of some function at some numbe...
 2.2.3.32: (a) Use a graph of to estimate the value of to two decimal places. ...
 2.2.8.32: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 2.2.4.32: Prove the statement using the $, # definition of limit.
 2.2.5.32: Use continuity to evaluate the limit
 2.2.6.32: Find the limit
 2.2.2.33: Determine and (a) by evaluating for values of that approach 1 from ...
 2.2.7.33: Each limit represents the derivative of some function at some numbe...
 2.2.3.33: Use the Squeeze Theorem to show that limxl0 !x . Illustrate by grap...
 2.2.8.33: The unemployment rate varies with time. The table (from the Bureau ...
 2.2.4.33: Verify that another possible choice of for showing that limxl3 x # ...
 2.2.5.33: Use continuity to evaluate the limit
 2.2.6.33: Find the limit
 2.2.2.34: (a) Find the vertical asymptotes of the function y ! x 2 ! 13x " 2x...
 2.2.7.34: Each limit represents the derivative of some function at some numbe...
 2.2.3.34: Use the Squeeze Theorem to show that limxl0sx 3 ! x 2 sin #x ! 0 Il...
 2.2.8.34: Let be the percentage of Americans under the age of 18 at time . Th...
 2.2.4.34: Verify, by a geometric argument, that the largest possible choice o...
 2.2.5.34: Use continuity to evaluate the limit
 2.2.6.34: Find the limit
 2.2.2.35: (a) Estimate the value of the limit limx l 0 !1 ! x"1&x to fivedeci...
 2.2.7.35: Each limit represents the derivative of some function at some numbe...
 2.2.3.35: If 4x " 9 ' f!x" ' x 2 " 4x ! 7 for x & 0limxl4 f!x"
 2.2.8.35: The graph of is given. State, with reasons, the numbers at which is...
 2.2.4.35: a) For the limit , use a graph to find a value of that corresponds ...
 2.2.5.35: Show that is continuous on !"$, $"
 2.2.6.35: Find the limit
 2.2.2.36: (a) By graphing the function and zooming in toward the point where ...
 2.2.7.36: Each limit represents the derivative of some function at some numbe...
 2.2.3.36: if 2x ' t!x" ' x x limxl1 t!x" 4 " x 2 ! 2 for all evaluatelimxl1 t
 2.2.8.36: The graph of is given. State, with reasons, the numbers at which is...
 2.2.4.36: prove that limx l21x ! 12
 2.2.5.36: Show that is continuous on !"$, $"
 2.2.6.36: Find the limit
 2.2.2.37: (a) Evaluate the function for 1, 0.8, 0.6, 0.4, 0.2, 0.1, and 0.05,...
 2.2.7.37: A particle moves along a straight line with equation of motion , wh...
 2.2.3.37: Prove that limxl0x 4 cos 2x ! 0.
 2.2.8.37: The graph of is given. State, with reasons, the numbers at which is...
 2.2.4.37: Prove that lim a % 0. x l a37. sx ! sa
 2.2.5.37: Find the numbers at which is discontinuous. At which of these numbe...
 2.2.6.37: (a) Estimate the value of by graphing the function . (b) Use a tabl...
 2.2.2.38: (a) Evaluate for , 0.5, 0.1, 0.05, 0.01, and 0.005. (c) Evaluate fo...
 2.2.7.38: A particle moves along a straight line with equation of motion , wh...
 2.2.3.38: Prove that limxl0! sx esin!##x" ! 0
 2.2.8.38: The graph of is given. State, with reasons, the numbers at which is...
 2.2.4.38: If is the Heaviside function defined in Example 6 in Section 2.2, p...
 2.2.5.38: Find the numbers at which is discontinuous. At which of these numbe...
 2.2.6.38: (a) Use a graph of to estimate the value of to one decimal place. (...
 2.2.2.39: Graph the function of Example 4 in the viewing rectangle '"1, 1( by...
 2.2.7.39: A warm can of soda is placed in a cold refrigerator. Sketch the gra...
 2.2.3.39: Find the limit, if it exists. If the limit does not exist, explain ...
 2.2.8.39: Graph the function . Zoom in repeatedly, first toward the point ($1...
 2.2.4.39: If the function is defined by f "x# ! 01if x is rationalif x is ir...
 2.2.5.39: Find the numbers at which is discontinuous. At which of these numbe...
 2.2.6.39: Find the horizontal and vertical asymptotes of each curve. If you h...
 2.2.2.40: In the theory of relativity, the mass of a particle with velocity i...
 2.2.7.40: A roast turkey is taken from an oven when its temperature has reach...
 2.2.3.40: Find the limit, if it exists. If the limit does not exist, explain ...
 2.2.8.40: Zoom in toward the points (1, 0), (0, 1), and ($1, 0) on the graph ...
 2.2.4.40: By comparing Definitions 2, 3, and 4, prove Theorem 1 in Section 2.3.
 2.2.5.40: The gravitational force exerted by the earth on a unit mass at a di...
 2.2.6.40: Find the horizontal and vertical asymptotes of each curve. If you h...
 2.2.2.41: Use a graph to estimate the equations of all the vertical asymptote...
 2.2.7.41: The table shows the estimated percentage of the population of Europ...
 2.2.3.41: Find the limit, if it exists. If the limit does not exist, explain ...
 2.2.8.41: The figure shows the graphs of , , and . Identify each curve, and e...
 2.2.4.41: How close to do we have to take so that "x & 3#4 % 10,000
 2.2.5.41: For what value of the constant is the function continuous on !"$, $...
 2.2.6.41: Find the horizontal and vertical asymptotes of each curve. If you h...
 2.2.2.42: (a) Use numerical and graphical evidence to guess the value of the ...
 2.2.7.42: The number of locations of a popular coffeehouse chain is given in ...
 2.2.3.42: Find the limit, if it exists. If the limit does not exist, explain ...
 2.2.8.42: The figure shows graphs of , , and . Identify each curve, and expla...
 2.2.4.42: Prove, using Definition 6, that limx l!31"x & 3#4 ! (
 2.2.5.42: Find the values of and that make continuous everywhere. f!x" !x 2 "...
 2.2.6.42: Find the horizontal and vertical asymptotes of each curve. If you h...
 2.2.7.43: The cost (in dollars) of producing units of a certain commodity is ...
 2.2.3.43: Find the limit, if it exists. If the limit does not exist, explain ...
 2.2.8.43: The figure shows the graphs of three functions. One is the position...
 2.2.4.43: Prove that limxl0& 43. ln x ! !(
 2.2.5.43: Which of the following functions has a removable discontinuity at ?...
 2.2.6.43: Find the horizontal and vertical asymptotes of each curve. If you h...
 2.2.7.44: If a cylindrical tank holds 100,000 gallons of water, which can be ...
 2.2.3.44: Find the limit, if it exists. If the limit does not exist, explain ...
 2.2.8.44: The figure shows the graphs of four functions. One is the position ...
 2.2.4.44: Suppose that and , whereis a real number. Prove each statement.(a)(...
 2.2.5.44: Suppose that a function is continuous on [0, 1] except at 0.25 and ...
 2.2.6.44: Find the horizontal and vertical asymptotes of each curve. If you h...
 2.2.7.45: The cost of producing x ounces of gold from a new gold mine is doll...
 2.2.3.45: The signum (or sign) function, denoted by sgn, is defined by sgn x ...
 2.2.8.45: Use the definition of a derivative to find and . Then graph , , and...
 2.2.5.45: If f !x" ! x c 2 ! 10 sin x how that there is a number suchthat f !...
 2.2.6.45: Estimate the horizontal asymptote of the function by graphing for ....
 2.2.7.46: The number of bacteria after t hours in a controlled laboratory exp...
 2.2.3.46: (a) Find and (b) Does exist? (c) Sketch the graph of . 47. Let . (a...
 2.2.8.46: Use the definition of a derivative to find and . Then graph , , and...
 2.2.5.46: Suppose is continuous on and the only solutions of the equation f !...
 2.2.6.46: (a) Graph the function How many horizontal and vertical asymptotes ...
 2.2.7.47: Let be the temperature (in ) in Dallas hours after midnight on June...
 2.2.3.47: (a) Find and (b) Does exist? (c) Sketch the graph of . 47. Let . (a...
 2.2.8.47: If , find , , , and . Graph , , , and on a common screen. Are the g...
 2.2.5.47: Use the Intermediate Value Theorem to show that there is a root of ...
 2.2.6.47: Find a formula for a function that satisfies the following conditions:
 2.2.7.48: The quantity (in pounds) of a gourmet ground coffee that is T sold ...
 2.2.3.48: 8. Let (a) Evaluate each of the following limits, if it exists. (i)...
 2.2.8.48: . (a) The graph of a position function of a car is shown, where s i...
 2.2.5.48: Use the Intermediate Value Theorem to show that there is a root of ...
 2.2.6.48: Find a formula for a function that has vertical asymptotes and and ...
 2.2.6.49: Find the limits as and as . Use this information, together with int...
 2.2.7.49: The quantity of oxygen that can dissolve in water depends on the te...
 2.2.3.49: if the symbol denotes the greatest integer function defined in Exam...
 2.2.8.49: Let f!x" ! s3 x (a) If , use Equation 2.7.5 to find . (b) Show that...
 2.2.5.49: Use the Intermediate Value Theorem to show that there is a root of ...
 2.2.6.50: Find the limits as and as . Use this information, together with int...
 2.2.7.50: The graph shows the influence of the temperature on the maximum sus...
 2.2.3.50: Let , . (a) Sketch the graph of (b) Evaluate each limit, if it exists.
 2.2.8.50: (a) If , show that does not exist. (b) If , find . (c) Show that ha...
 2.2.5.50: Use the Intermediate Value Theorem to show that there is a root of ...
 2.2.6.51: Find the limits as and as . Use this information, together with int...
 2.2.7.51: Determine whether f!!0" exists f!x" ! %x sin1x if x " 00 if x ! 051.
 2.2.3.51: If f!x" ! &x ' ! &"x ' show that limxl2 f!x" exists but is notequal...
 2.2.8.51: Show that the function f!x" ! ( x $ 6 is not differentiable at 6. F...
 2.2.5.51: (a) Prove that the equation has at least one real root. (b) Use you...
 2.2.6.52: Find the limits as and as . Use this information, together with int...
 2.2.7.52: Determine whether f!!0" exists f!x" ! %x 2 sin1x if x " 00 if x ! 0
 2.2.3.52: In the theory of relativity, the Lorentz contraction formula expres...
 2.2.8.52: Where is the greatest integer function f !x" ! ) x not differentiab...
 2.2.5.52: (a) Prove that the equation has at least one real root. (b) Use you...
 2.2.6.53: (a) Use the Squeeze Theorem to evaluate . ; (b) Graph . How many ti...
 2.2.3.53: If is a polynomial, show that limxla p!x" ! p!a"
 2.2.8.53: (a) Sketch the graph of the function . (b) For what values of is di...
 2.2.5.53: (a) Prove that the equation has at least one real root. (b) Use you...
 2.2.6.54: By the end behavior of a function we mean the behavior of its value...
 2.2.3.54: If r is a rational function, use Exercise 53 to show that lim for e...
 2.2.8.54: The lefthand and righthand derivatives of at are defined by and i...
 2.2.5.54: (a) Prove that the equation has at least one real root. (b) Use you...
 2.2.6.55: Let and be polynomials. Find if the degree of is (a) less than the ...
 2.2.3.55: If lim f!x" f!x" " 8x " 1xl1 find limxl1lim f!x"
 2.2.8.55: Recall that a function is called even if for all in its domain and ...
 2.2.5.55: Prove that is continuous at if and only if limh l 0 f !a ! h" ! f!a"
 2.2.6.56: Make a rough sketch of the curve ( an integer) for the following fi...
 2.2.3.56: If limxl0 f!x"x 2 ! 5 f!x"x 2 ! 5
 2.2.8.56: When you turn on a hotwater faucet, the temperature of the water d...
 2.2.5.56: To prove that sine is continuous, we need to show that for every re...
 2.2.6.57: Find if, limxl! f"x# for all x % 1 10ex " 212ex $ f"x# $5sxsx " 1
 2.2.3.57: If f!x" ! $x 20if x is rationalif x is irrational
 2.2.8.57: Let be the tangent line to the parabola at the point . The angle of...
 2.2.5.57: Prove that cosine is a continuous function
 2.2.6.58: (a) A tank contains 5000 L of pure water. Brine that contains 30 g ...
 2.2.3.58: Show by means of an example tha
 2.2.5.58: (a) Prove Theorem 4, part 3. (b) Prove Theorem 4, part 5
 2.2.6.59: In Chapter 9 we will be able to show, under certain assumptions, th...
 2.2.3.59: Show by means of an example that limxla ( f!x"t!x" mayexist even th...
 2.2.5.59: For what values of is continuous? f !x" ! +01if x is rationalif x i...
 2.2.6.60: (a) By graphing and y ! 0.1 on a common screen, discover how large ...
 2.2.3.60: Evaluate xl2s6 " x " 2s3 " x " 1
 2.2.5.60: For what values of is continuous? !x" ! +0xif x is rationalif x is ...
 2.2.6.61: Use a graph to find a number such that if x % Nthen & 3x 2 # 12x 2 ...
 2.2.3.61: Is there a number a such that imx l"23x 2 ! ax ! a ! 3x 2 ! x " 2 e...
 2.2.5.61: Is there a number that is exactly 1 more than its cube?I
 2.2.6.62: For the limit imx l !s4x 2 # 1x # 1 ! 2 illustrate Definition 7 by ...
 2.2.3.62: The figure shows a fixed circle with equation and a shrinking circl...
 2.2.5.62: If and are positive numbers, prove that the equation x 3 ! 2x 2 " 1...
 2.2.6.63: For the limit limx l"!s4x 2 # 1x # 1 ! "2
 2.2.5.63: Show that the function f!x" ! +x 4 sin!1#x"0if x " 0if x ! 0
 2.2.6.64: For the limit limxl!2x # 1sx # 1 ! !illustrate Definition 9 by find...
 2.2.5.64: (a) Show that the absolute value function is continuous everywhere....
 2.2.6.65: (a) How large do we have to take so that ? (b) Taking in Theorem 5,...
 2.2.5.65: A Tibetan monk leaves the monastery at 7:00 AM and takes his usual ...
 2.2.6.66: (a) How large do we have to take so that ? (b) Taking in Theorem 5,...
 2.2.6.67: Use Definition 8 to prove thatlimx l"!1x ! 0
 2.2.6.68: Prove, using Definition 9,
 2.2.6.69: Prove, using Definition 9,
 2.2.6.70: Formulate a precise definition of limx l"!f "x# ! "! Then use your ...
 2.2.6.71: Prove that limxl!f"x# ! limtl0# f "1!t# ndif these limits exist.lim...
Solutions for Chapter 2: Limits and Derivatives
Full solutions for Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign)  6th Edition
ISBN: 9780495011699
Solutions for Chapter 2: Limits and Derivatives
Get Full SolutionsThis textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign), edition: 6. Since 402 problems in chapter 2: Limits and Derivatives have been answered, more than 17288 students have viewed full stepbystep solutions from this chapter. Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780495011699. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2: Limits and Derivatives includes 402 full stepbystep solutions.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Acceleration due to gravity
g ? 32 ft/sec2 ? 9.8 m/sec

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Central angle
An angle whose vertex is the center of a circle

Complex conjugates
Complex numbers a + bi and a  bi

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Convenience sample
A sample that sacrifices randomness for convenience

Endpoint of an interval
A real number that represents one “end” of an interval.

Horizontal component
See Component form of a vector.

Identity
An equation that is always true throughout its domain.

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Multiplication property of equality
If u = v and w = z, then uw = vz

PH
The measure of acidity

Positive angle
Angle generated by a counterclockwise rotation.

Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

Second
Angle measure equal to 1/60 of a minute.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.