 1.1.6.1: For the function whose graph is given, state the following. (a) (b)...
 1.1.2.1: (a) Find an equation for the family of linear functions with slope ...
 1.1: (a) What is a function? What are its domain and range? f A t B (b) ...
 1.1.3.1: If a ball is thrown into the air with a velocity of 40 fts, its t2 ...
 1.1.4.1: Given that find the limits that exist. If the limit does not exist,...
 1.1.5.1: Write an equation that expresses the fact that a function is contin...
 1.1.1.1: The graph of a function is given. (a) State the value of . (b) Esti...
 1.1.6.2: For the function t whose graph is given, state the following. (a) (...
 1.1.2.2: What do all members of the family of linear functions have in commo...
 1.2: Discuss four ways of representing a function. Illustrate your discu...
 1.1.3.2: If an arrow is shot upward on the moon with a velocity of 58 ms, it...
 1.1.4.2: The graphs of and t are given. Use them to evaluate each limit, if ...
 1.1.5.2: If is continuous on , what can you say about its graph?
 1.1.1.2: The graphs of and t are given. (a) State the values of and . (b) Fo...
 1.1.6.3: Sketch the graph of an example of a function that satisfies all of ...
 1.1.2.3: What do all members of the family of linear functions have in commo...
 1.3: (a) What is an even function? How can you tell if a function is eve...
 1.1.3.3: Use the given graph of to state the value of each quantity, if it e...
 1.1.4.3: Evaluate the limit and justify each step by indicating the appropri...
 1.1.5.3: a) From the graph of , state the numbers at which is discontinuous ...
 1.1.1.3: Determine whether the curve is the graph of a function of . If it i...
 1.1.6.4: Sketch the graph of an example of a function that satisfies all of ...
 1.1.2.4: Find expressions for the quadratic functions whose graphs are shown.
 1.4: What is a mathematical model?
 1.1.3.4: For the function whose graph is given, state the value of each quan...
 1.1.4.4: Evaluate the limit and justify each step by indicating the appropri...
 1.1.5.4: From the graph of , state the intervals on which is continuous.
 1.1.1.4: Determine whether the curve is the graph of a function of . If it i...
 1.1.6.5: Sketch the graph of an example of a function that satisfies all of ...
 1.1.2.5: Find an expression for a cubic function if and f1 f 0 f 2 0 f f1 6 y
 1.5: Give an example of each type of function. (a) Linear function (b) P...
 1.1.3.5: For the function whose graph is given, state the value of each quan...
 1.1.4.5: Evaluate the limit and justify each step by indicating the appropri...
 1.1.5.5: Sketch the graph of a function that is continuous everywhere except...
 1.1.1.5: Determine whether the curve is the graph of a function of . If it i...
 1.1.6.6: Sketch the graph of an example of a function that satisfies all of ...
 1.1.2.6: Some scientists believe that the average surface temperature of the...
 1.6: Sketch by hand, on the same axes, the graphs of the following funct...
 1.1.3.6: ketch the graph of the following function and use it to determine t...
 1.1.4.6: Evaluate the limit and justify each step by indicating the appropri...
 1.1.5.6: Sketch the graph of a function that has a jump discontinuity at and...
 1.1.1.6: Determine whether the curve is the graph of a function of . If it i...
 1.1.6.7: Sketch the graph of an example of a function that satisfies all of ...
 1.1.2.7: If the recommended adult dosage for a drug is (in mg), then to dete...
 1.7: Sketch by hand, on the same axes, the graphs of the following funct...
 1.1.3.7: Sketch the graph of an example of a function that satisfies all of ...
 1.1.4.7: Evaluate the limit and justify each step by indicating the appropri...
 1.1.5.7: A parking lot charges $3 for the first hour (or part of an hour) an...
 1.1.1.7: The graph shown gives the weight of a certain person as a function ...
 1.1.6.8: Sketch the graph of an example of a function that satisfies all of ...
 1.1.2.8: The manager of a weekend flea market knows from past experience tha...
 1.8: Suppose that has domain and has domain . (a) What is the domain of ...
 1.1.3.8: Sketch the graph of an example of a function that satisfies all of ...
 1.1.4.8: Evaluate the limit and justify each step by indicating the appropri...
 1.1.5.8: Explain why each function is continuous or discontinuous. (a) The t...
 1.1.1.8: The graph shown gives a salesmans distance from his home as a funct...
 1.1.6.9: Guess the value of the limit by evaluating the function for and . T...
 1.1.2.9: The relationship between the Fahrenheit and Celsius temperature sca...
 1.9: How is the composite function defined? What is its domain?
 1.1.3.9: Sketch the graph of an example of a function that satisfies all of ...
 1.1.4.9: Evaluate the limit and justify each step by indicating the appropri...
 1.1.5.9: If and are continuous functions with and limx l 3 2 f x tx 4 t3 f t...
 1.1.1.9: You put some ice cubes in a glass, fill the glass with cold water, ...
 1.1.6.10: Determine and (a) by evaluating for values of that approach 1 from ...
 1.1.2.10: Jason leaves Detroit at 2:00 PM and drives at a constant speed west...
 1.10: Suppose the graph of is given. Write an equation for each of the gr...
 1.1.3.10: Sketch the graph of an example of a function that satisfies all of ...
 1.1.4.10: (a) What is wrong with the following equation? (b) In view of part ...
 1.1.5.10: Use the definition of continuity and the properties of limits to sh...
 1.1.1.10: Sketch a rough graph of the number of hours of daylight as a functi...
 1.1.6.11: Use a graph to estimate all the vertical and horizontal asymptotes ...
 1.1.2.11: Biologists have noticed that the chirping rate of crickets of a cer...
 1.11: Explain what each of the following means and illustrate with a sket...
 1.1.3.11: Guess the value of the limit (if it exists) by evaluating the funct...
 1.1.4.11: Evaluate the limit, if it exists. limxl2x 2 x 6x 2li
 1.1.5.11: Use the definition of continuity and the properties of limits to sh...
 1.1.1.11: Sketch a rough graph of the outdoor temperature as a function of ti...
 1.1.6.12: (a) Use a graph of to estimate the value of correct to two decimal ...
 1.1.2.12: The manager of a furniture factory finds that it costs $2200 to man...
 1.12: Describe several ways in which a limit can fail to exist. Illustrat...
 1.1.3.12: Guess the value of the limit (if it exists) by evaluating the funct...
 1.1.4.12: Evaluate the limit, if it exists. imxl4x 2 5x 4x2 3x 4lim
 1.1.5.12: Use the definition of continuity and the properties of limits to sh...
 1.1.1.12: Sketch a rough graph of the market value of a new car as a function...
 1.1.6.13: Find the limit limxl3x 2x 3fx
 1.1.2.13: At the surface of the ocean, the water pressure is the same as the ...
 1.13: State the following Limit Laws. (a) Sum Law (b) Difference Law (c) ...
 1.1.3.13: Guess the value of the limit (if it exists) by evaluating the funct...
 1.1.4.13: Evaluate the limit, if it exists. limxl2x 2 x 6x 2li
 1.1.5.13: Explain why the function is discontinuous at . Sketch the graph of ...
 1.1.1.13: Sketch the graph of the amount of a particular brand of coffee sold...
 1.1.6.14: Find the limit limxl56x 5l
 1.1.2.14: The monthly cost of driving a car depends on the number of miles dr...
 1.14: What does the Squeeze Theorem say?
 1.1.3.14: Guess the value of the limit (if it exists) by evaluating the funct...
 1.1.4.14: Evaluate the limit, if it exists. limxl 4x 2 4xx 2 3x 4li
 1.1.5.14: Explain why the function is discontinuous at . Sketch the graph of ...
 1.1.1.14: You place a frozen pie in an oven and bake it for an hour. Then you...
 1.1.6.15: Find the limit lim cot x xl12 xx 12 15.
 1.1.2.15: Suppose the graph of is given. Write equations for the 19. f graphs...
 1.15: (a) What does it mean for f to be continuous at a? (b) What does it...
 1.1.3.15: Use a table of values to estimate the value of the limit. If you ha...
 1.1.4.15: Evaluate the limit, if it exists. limtl3t2 92t2 7t 315.
 1.1.5.15: Explain why the function is discontinuous at . Sketch the graph of ...
 1.1.1.15: A homeowner mows the lawn every Wednesday afternoon. Sketch a rough...
 1.1.1.16: A jet takes off from an airport and lands an hour later at another ...
 1.1.6.16: Find the limit limxl lim cot x x
 1.1.2.16: Explain how the following graphs are obtained from the graph of . (...
 1.16: What does the Intermediate Value Theorem say?
 1.1.3.16: Use a table of values to estimate the value of the limit. If you ha...
 1.1.4.16: Evaluate the limit, if it exists. imxl1x 2 4xx 2 3x 4lim
 1.1.5.16: Explain why the function is discontinuous at . Sketch the graph of ...
 1.1.1.17: If , find , , , ,[ fa] fa h 2 fa , 2 f a 1 2f a f2a fx 3x f2 f 2
 1.1.6.17: Find the limit lim x l2 sec xlim
 1.1.2.17: The graph of is given. Match each equation with its graph and give ...
 1.17: (a) What does it mean to say that the line is a vertical asymptote ...
 1.1.3.17: Use a table of values to estimate the value of the limit. If you ha...
 1.1.4.17: Evaluate the limit, if it exists. limhl04 h2 16hlim
 1.1.5.17: Explain, using Theorems 4, 5, 6, and 8, why the func c t , . tion ...
 1.1.1.18: A spherical balloon with radius inches has volume . Find a function...
 1.1.6.18: Find the limit imxl3x 5x 4l
 1.1.2.18: The graph of is given. Draw the graphs of the following functions. ...
 1.18: If f is continuous on and and then there exists a number r such tha...
 1.1.3.18: Use a table of values to estimate the value of the limit. If you ha...
 1.1.4.18: Evaluate the limit, if it exists. limhl0s1 h 1hl
 1.1.5.18: Explain, using Theorems 4, 5, 6, and 8, why the func c t , . tion ...
 1.1.1.19: Evaluate the difference quotient for the given function. Simplify y...
 1.1.6.19: Find the limit limxlx 3 5x2x 3 x 2 419
 1.1.2.19: The graph of is given. Use it to graph the following functions. (a)...
 1.19: Let be a function such that . Then there exists a number such that ...
 1.1.3.19: (a) By graphing the function and zooming in toward the point where ...
 1.1.4.19: Evaluate the limit, if it exists. limxl2x 2x 3 819
 1.1.5.19: Explain, using Theorems 4, 5, 6, and 8, why the func c t , . tion ...
 1.1.1.20: Evaluate the difference quotient for the given function. Simplify y...
 1.1.6.20: Find the limit limtlt2 2t3 t2 1lim
 1.1.2.20: (a) How is the graph of related to the graph of ? Use your answer a...
 1.20: If for all and exists, then limx l 0 f x 1.
 1.1.3.20: (a) Estimate the value of by graphing the function . State your ans...
 1.1.4.20: Evaluate the limit, if it exists. imxl1x 2 2x 1x 4 1lim
 1.1.5.20: Explain, using Theorems 4, 5, 6, and 8, why the func c t , . tion ...
 1.1.1.21: Evaluate the difference quotient for the given function. Simplify y...
 1.1.6.21: Find the limit limul 4u4 5u2 22u2 1limt
 1.1.2.21: Graph the function by hand, not by plotting points, but by starting...
 1.21: The graph of is given. (a) Find each limit, or explain why it does ...
 1.1.3.21: (a) Evaluate the function for 1, 0.8, 0.6, 0.4, 0.2, 0.1, and 0.05,...
 1.1.4.21: Evaluate the limit, if it exists. limxl7sx 2 3x 7li
 1.1.5.21: Explain, using Theorems 4, 5, 6, and 8, why the func c t , . tion ...
 1.1.1.22: Evaluate the difference quotient for the given function. Simplify y...
 1.1.6.22: Find the limit limxlx 2s9x 2 1l
 1.1.2.22: Graph the function by hand, not by plotting points, but by starting...
 1.22: Sketch the graph of an example of a function that satisfies all of ...
 1.1.3.22: (a) Evaluate for , 0.5, 0.1, 0.05, 0.01, and 0.005. (b) Guess the v...
 1.1.4.22: Evaluate the limit, if it exists. limhl 03 h1 31hlim
 1.1.5.22: Explain, using Theorems 4, 5, 6, and 8, why the func c t , . tion ...
 1.1.1.23: Find the domain of the function. f x x 3x 1 fx
 1.1.6.23: Find the limit limxl(s9x 23. 2 x 3x)
 1.1.2.23: Graph the function by hand, not by plotting points, but by starting...
 1.23: Find the limit. imt l 0t3tan3 2t
 1.1.3.23: Use the given graph of to find a number such that x x 2 0.5 0.2 fx
 1.1.4.23: Evaluate the limit, if it exists. lim xl4141x4 xli
 1.1.5.23: Locate the discontinuities of the function and illustrate by graphi...
 1.1.1.24: Find the domain of the function. f x 5x 4 x 2 3x 2 f x
 1.1.6.24: Find the limit imxl(sx 2 ax sx2 bx )lim
 1.1.2.24: Graph the function by hand, not by plotting points, but by starting...
 1.24: Find the limit. imt l 0t3tan3 2t
 1.1.3.24: Use the given graph of to find a number such that x 1 2 f
 1.1.4.24: Evaluate the limit, if it exists. limtl 0 1t 1t2 tl
 1.1.5.24: Locate the discontinuities of the function and illustrate by graphi...
 1.1.1.25: Find the domain of the function. ft st s 3 t f x
 1.1.6.25: Find the limit limxl cos x
 1.1.2.25: Graph the function by hand, not by plotting points, but by starting...
 1.25: Find the limit. "Find the limit. imt l 0t3tan3 2t"
 1.1.3.25: Use a graph to find a number such that if then x 2 s4x 1 3 0.5
 1.1.4.25: (a) Estimate the value of by graphing the function . (b) Make a tab...
 1.1.5.25: Use continuity to evaluate the limit. im 26. sinx sin x xl4 5 sx s5...
 1.1.1.26: Find the domain of the function. tu su s4 u ft
 1.1.6.26: Find the limit limxlsin2x
 1.1.2.26: Graph the function by hand, not by plotting points, but by starting...
 1.26: Find the limit. limxl1x 2 9x 2 2x 3lim
 1.1.3.26: Use a graph to find a number such that if then x 2  0.1 6
 1.1.4.26: missing problem
 1.1.5.26: Use continuity to evaluate the limit. lim xl lim 26. sinx sin x xl4
 1.1.1.27: Find the domain of the function. hx 1 s 4 x 2 5x 27.
 1.1.6.27: Find the limit limx l (x sx )
 1.1.2.27: Graph the function by hand, not by plotting points, but by starting...
 1.27: Find the limit. limhl0h 13 1hlim
 1.1.3.27: A machinist is required to manufacture a circular metal disk with a...
 1.1.4.27: missing problem
 1.1.5.27: Show that is continuous on . fx x 2 if x 1sx if x 1f
 1.1.1.28: Find the domain and range and sketch the graph of the function hx s...
 1.1.6.28: Find the limit imxlx 3 2x 35 2x2 lim
 1.1.2.28: Graph the function by hand, not by plotting points, but by starting...
 1.28: Find the limit. limtl2t2 4t3 8l
 1.1.3.28: A crystal growth furnace is used in research to determine how best ...
 1.1.4.28: missing problem
 1.1.5.28: Show that is continuous on . f x sin x if x 4cos x if x 4fx
 1.1.1.29: Find the domain and sketch the graph of the function f x 5 x
 1.1.6.29: Find the limit lim xl x 4 x 5lim
 1.1.2.29: Graph the function by hand, not by plotting points, but by starting...
 1.29: Find the limit. limrl9srr 94li
 1.1.3.29: Prove the statement using the definition of limit and illustrate wi...
 1.1.4.29: lim xl0 sx 1 sin2 2x 0 lim xl0 x 4 cos 2 x 0. 2x tx x x limxl1 tx 4...
 1.1.5.29: Find the numbers at which the function is discontinuous. At which o...
 1.1.1.30: Find the domain and sketch the graph of the function Fx 1 2 f x 5 x...
 1.1.6.30: Find the limit limx l x 2 x 4 lim xl
 1.1.2.30: Graph the function by hand, not by plotting points, but by starting...
 1.30: Find the limit. limvl 44 v 4 v lim
 1.1.3.30: Prove the statement using the definition of limit and illustrate wi...
 1.1.4.30: missing problem
 1.1.5.30: The gravitational force exerted by the Earth on a unit mass at a di...
 1.1.1.31: Find the domain and sketch the graph of the function f t t 2 6t Fx
 1.1.6.31: Find the limit imxlx x 3 x 51 x 2 x 4lim
 1.1.2.31: Graph the function by hand, not by plotting points, but by starting...
 1.31: Find the limit. lims l164 sss 16l
 1.1.3.31: Prove the statement using the definition of limit and illustrate wi...
 1.1.4.31: missing problem
 1.1.5.31: For what value of the constant is the function continuous on ? fx c...
 1.1.1.32: Find the domain and sketch the graph of the function Ht 4 t 2 2 t f t
 1.1.6.32: (a) Graph the function How many horizontal and vertical asymptotes ...
 1.1.2.32: Graph the function by hand, not by plotting points, but by starting...
 1.32: Find the limit. limv l2v 2 2v 8v 4 16li
 1.1.3.32: Prove the statement using the definition of limit and illustrate wi...
 1.1.4.32: missing problem
 1.1.5.32: Find the constant that makes continuous on tx x 2 c 2 cx 20 if x 4 ...
 1.1.1.33: Find the domain and sketch the graph of the function tx sx 5 Ht
 1.1.6.33: Find the horizontal and vertical asymptotes of each curve. Check yo...
 1.1.2.33: Graph the function by hand, not by plotting points, but by starting...
 1.33: Find the limit. limx l 1 2x x 21 x 2x 2lim
 1.1.3.33: Prove the statement using the definition of limit. lim x l3 x 5 3 5
 1.1.4.33: x 1 t lim xl1 lim tx xl1 lim tx xl1 tx lim xl0 lim tx xl1 lim tx xl...
 1.1.5.33: Which of the following functions has a removable discontinuity at ?...
 1.1.1.34: Find the domain and sketch the graph of the function Fx 2x 1 tx s
 1.1.6.34: Find the horizontal and vertical asymptotes of each curve. Check yo...
 1.1.2.34: Graph the function by hand, not by plotting points, but by starting...
 1.34: Find the limit. limxl1 2x 2 x 45 x 3x 4 lim
 1.1.3.34: Prove the statement using the definition of limit. im x l 6 x 4 3 9...
 1.1.4.34: missing problem
 1.1.5.34: Suppose that a function is continuous on [0, 1] except at 0.25 and ...
 1.1.1.35: Find the domain and sketch the graph of the function G 2 x 3x x x 35.
 1.1.6.35: (a) Estimate the value of by graphing the function . (b) Use a tabl...
 1.1.2.35: Find , , , and and state their domains. tx 3x f x x 2 1 3 2x 2 f t f
 1.35: Find the limit. limxl(sx 2 4x 1 x)l
 1.1.3.35: Prove the statement using the definition of limit. lim 7 x l5 4 3x ...
 1.1.4.35: missing problem
 1.1.5.35: If , show that there is a number such that .
 1.1.1.36: Find the domain and sketch the graph of the function tx x x G 2 x
 1.1.6.36: (a) Use a graph of to estimate the value of to one decimal place. (...
 1.1.2.36: Find , , , and and state their domains. fx s1 x tx s1 x tx 3x f
 1.36: Find the limit. limxl1 1x 11x 2 3x 2 lim
 1.1.3.36: Prove the statement using the definition of limit. lim x l3 x 2 x 1...
 1.1.4.36: missing problem
 1.1.5.36: Use the Intermediate Value Theorem to prove that there is a positiv...
 1.1.1.37: Find the domain and sketch the graph of the function f x x 2 1 x if...
 1.1.6.37: Estimate the horizontal asymptote of the function by graphing for ....
 1.1.2.37: Find the functions (a) , (b) , (c) , and (d) and their domains. f x...
 1.37: Find the limit. limxl0cot 2xcsc x
 1.1.3.37: Prove the statement using the definition of limit. im c c x l a x a l
 1.1.4.37: missing problem
 1.1.5.37: Use the Intermediate Value Theorem to show that there is a root of ...
 1.1.1.38: Find the domain and sketch the graph of the function f x 3 1 2 x 2x...
 1.1.6.38: Find a formula for a function that has vertical asymptotes and and ...
 1.1.2.38: Find the functions (a) , (b) , (c) , and (d) and their domains. fx ...
 1.38: Find the limit. imt l 0t3tan3 2t
 1.1.3.38: Prove the statement using the definition of limit. lim x l a lim c c x
 1.1.4.38: missing problem
 1.1.5.38: Use the Intermediate Value Theorem to show that there is a root of ...
 1.1.1.39: Find the domain and sketch the graph of the function f x x 2 x 2 if...
 1.1.6.39: Find a formula for a function that satisfies the following conditio...
 1.1.2.39: Find the functions (a) , (b) , (c) , and (d) and their domains. f x...
 1.39: Use graphs to discover the asymptotes of the curve. Then prove what...
 1.1.3.39: Prove the statement using the definition of limit. lim 3 0 x l 0 x w
 1.1.4.39: (a) If the symbol denotes the greatest integer function defined in ...
 1.1.5.39: Use the Intermediate Value Theorem to show that there is a root of ...
 1.1.1.40: Find the domain and sketch the graph of the function f x 1 3x 2 7 2...
 1.1.6.40: By the end behavior of a function we mean the behavior of its value...
 1.1.2.40: Find the functions (a) , (b) , (c) , and (d) and their domains. tx ...
 1.40: Use graphs to discover the asymptotes of the curve. Then prove what...
 1.1.3.40: Prove the statement using the definition of limit. lim x l 0 x lim 3 0
 1.1.4.40: Let . (a) Sketch the graph of (b) If is an integer, evaluate (i) (i...
 1.1.5.40: Use the Intermediate Value Theorem to show that there is a root of ...
 1.1.1.41: Find an expression for the function whose graph is the given curve....
 1.1.6.41: Let and be polynomials. Find if the degree of is (a) less than the ...
 1.1.2.41: Find the functions (a) , (b) , (c) , and (d) and their domains. x 2...
 1.41: If for , find
 1.1.3.41: Prove the statement using the definition of limit. lim 9 x 0 x l 0 ...
 1.1.4.41: If , show that exists but is not equal to .
 1.1.5.41: (a) Prove that the equation has at least one real root. (b) Use you...
 1.1.5.42: (a) Prove that the equation has at least one real root. (b) Use you...
 1.1.1.42: Find an expression for the function whose graph is the given curve....
 1.1.6.42: Make a rough sketch of the curve ( an integer) for the following fi...
 1.1.2.42: Find the functions (a) , (b) , (c) , and (d) and their domains. tx ...
 1.1.3.42: Prove the statement using the definition of limit. lim xl9 s 4 lim ...
 1.1.4.42: In the theory of relativity, the Lorentz contraction formula expres...
 1.1.5.43: (a) Prove that the equation has at least one real root. (b) Use you...
 1.1.1.43: Find an expression for the function whose graph is the given curve....
 1.1.6.43: Find if, for all , 4x 1x fx 4x 2 3xx 243.
 1.1.2.43: Find (cannot be copied)
 1.1.3.43: Prove the statement using the definition of limit. x 2 9 x 3 x 3 li...
 1.1.4.43: Find the limit. limxl0sin 3xx
 1.1.5.44: (a) Prove that the equation has at least one real root. (b) Use you...
 1.1.1.44: Find an expression for the function whose graph is the given curve....
 1.1.6.44: In the theory of relativity, the mass of a particle with velocity i...
 1.1.2.44: Find (cannot be copied)
 1.1.3.44: Prove the statement using the definition of limit. lim x 3 1 x l3 x...
 1.1.4.44: Find the limit. limxl0sin 4xsin 6x
 1.1.5.45: Is there a number that is exactly 1 more than its cube?
 1.1.1.45: A rectangle has perimeter 20 m. Express the area of the rectangle a...
 1.1.6.45: (a) A tank contains 5000 L of pure water. Brine that contains 30 g ...
 1.1.2.45: Express the function in the form f t. f Fx x Fx sin(sx ) 2 110 f t.
 1.1.3.45: (a) For the limit , use a graph to find a value of that corresponds...
 1.1.4.45: Find the limit. imtl0tan 6tsin 2t
 1.1.5.46: (a) Show that the absolute value function is continuous everywhere....
 1.1.1.46: A rectangle has area 16 m . Express the perimeter of the rectangle ...
 1.1.6.46: (a) Show that . ; (b) By graphing the function in part (a) and the ...
 1.1.2.46: Express the function in the form f t. f Fx sin(sx ) 2
 1.1.3.46: If is the Heaviside function defined in Example 6, prove, using Def...
 1.1.4.46: Find the limit. limtl0sin2 3tt2
 1.1.5.47: A Tibetan monk leaves the monastery at 7:00 AM and takes his usual ...
 1.1.1.47: Express the area of an equilateral triangle as a function of the le...
 1.1.6.47: How close to do we have to take so that x 34 10,0003
 1.1.2.47: Express the function in the form f t. f ut scos t 48.
 1.1.4.47: Find the limit. im x cot x l0sin tan
 1.1.1.48: Express the surface area of a cube as a function of its volume.
 1.1.6.48: Prove, using Definition 6, that imxl31x 34 1
 1.1.2.48: Express the function in the form f t. f ut tan t 1 tan t ut
 1.1.4.48: Find the limit. limxl0lim x cot x
 1.1.1.49: An open rectangular box with volume 2 m has a square base. Express ...
 1.1.6.49: Prove that . imxl15x 1 49. 3
 1.1.2.49: Express the function in the form f t h. ut H x 1 3x 2 f
 1.1.4.49: If is a polynomial, show that .
 1.1.1.50: A taxi company charges two dollars for the first mile (or part of a...
 1.1.6.50: For the limit illustrate Definition 7 by finding values of that cor...
 1.1.2.50: Express the function in the form f t h. ut Hx s 8 2 x H x 1
 1.1.4.50: If r is a rational function, use Exercise 49 to show that limxla rx...
 1.1.1.51: In a certain country, income tax is assessed as follows. There is n...
 1.1.6.51: Use a graph to find a number such that whenever x N
 1.1.2.51: Express the function in the form f t h. ut Hx sec4 (sx ) Hx
 1.1.4.51: To prove that sine has the Direct Substitution Property we need to ...
 1.1.1.52: The functions in Example 6 and Exercises 50 and 51(a) are called st...
 1.1.6.52: For the limit illustrate Definition 8 by finding a value of that co...
 1.1.2.52: Use the table to evaluate each expression. (a) (b) (c) (d) (e) (f )
 1.1.4.52: Prove that cosine has the Direct Substitution Property.
 1.1.1.53: Graphs of and are shown. Decide whether each function is even, odd,...
 1.1.6.53: (a) How large do we have to take so that ? (b) Taking in (5), we ha...
 1.1.2.53: Use the given graphs of and to evaluate each expression, or explain...
 1.1.4.53: Show by means of an example that may exist even though neither nor ...
 1.1.1.54: Graphs of and are shown. Decide whether each function is even, odd,...
 1.1.6.54: Prove, using Definition 8, that .
 1.1.2.54: A spherical balloon is being inflated and the radius of the balloon...
 1.1.4.54: Show by means of an example that may exist even though neither nor ...
 1.1.1.55: (a) If the point is on the graph of an even function, what other po...
 1.1.6.55: Prove that and if these limits exist. lim x l fx lim tl0 f1t lim x ...
 1.1.2.55: A stone is dropped into a lake, creating a circular ripple that tra...
 1.1.4.55: Is there a number a such that exists? If so, find the value of a an...
 1.1.1.56: A function has domain and a portion of its graph is shown. (a) Comp...
 1.1.2.56: An airplane is flying at a speed of at an altitude of one mile and ...
 1.1.4.56: The figure shows a fixed circle with equation and a shrinking circl...
 1.1.1.57: Determine whether is even, odd, or neither. If you have a graphing ...
 1.1.2.57: The Heaviside function H is defined by It is used in the study of e...
 1.1.1.58: Determine whether is even, odd, or neither. If you have a graphing ...
 1.1.2.58: The Heaviside function defined in Exercise 57 can also be used to d...
 1.1.1.59: Determine whether is even, odd, or neither. If you have a graphing ...
 1.1.2.59: Let and be linear functions with equations and . Is also a linear f...
 1.1.1.60: Determine whether is even, odd, or neither. If you have a graphing ...
 1.1.2.60: If you invest dollars at 4% interest compounded annually, then the ...
 1.1.1.61: Determine whether is even, odd, or neither. If you have a graphing ...
 1.1.2.61: (a) If and , find a function such that . (Think about what operatio...
 1.1.1.62: Determine whether is even, odd, or neither. If you have a graphing ...
 1.1.2.62: If and , find a function such that .
 1.1.2.63: (a) Suppose and are even functions. What can you say about and ? (b...
 1.1.2.64: Suppose is even and is odd. What can you say about ?
 1.1.2.65: Suppose t is an even function and let . Is h always an even function?
 1.1.2.66: Suppose t is an odd function and let . Is h always an odd function?...
Solutions for Chapter 1: FUNCTIONS AND LIMITS
Full solutions for Essential Calculus (Available Titles CengageNOW)  1st Edition
ISBN: 9780495014423
Solutions for Chapter 1: FUNCTIONS AND LIMITS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Essential Calculus (Available Titles CengageNOW) was written by and is associated to the ISBN: 9780495014423. Chapter 1: FUNCTIONS AND LIMITS includes 373 full stepbystep solutions. Since 373 problems in chapter 1: FUNCTIONS AND LIMITS have been answered, more than 17202 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Essential Calculus (Available Titles CengageNOW), edition: 1.

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Arctangent function
See Inverse tangent function.

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

Cosine
The function y = cos x

Extracting square roots
A method for solving equations in the form x 2 = k.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Normal curve
The graph of ƒ(x) = ex2/2

Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

Product of matrices A and B
The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Radicand
See Radical.

RRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the righthand end point of each subinterval.

Subtraction
a  b = a + (b)

Unbounded interval
An interval that extends to ? or ? (or both).