 1.8.1: Use Figure 1.94 to give approximate values for the following limits...
 1.8.2: Use Figure 1.95 to estimate the following limits, if they exist. (a...
 1.8.3: Using Figures 1.96 and 1.97, estimate (a) lim x1 (f(x) + g(x)) (b) ...
 1.8.4: In Exercises 49, draw a possible graph of f(x). Assume f(x) is defi...
 1.8.5: In Exercises 49, draw a possible graph of f(x). Assume f(x) is defi...
 1.8.6: In Exercises 49, draw a possible graph of f(x). Assume f(x) is defi...
 1.8.7: In Exercises 49, draw a possible graph of f(x). Assume f(x) is defi...
 1.8.8: In Exercises 49, draw a possible graph of f(x). Assume f(x) is defi...
 1.8.9: In Exercises 49, draw a possible graph of f(x). Assume f(x) is defi...
 1.8.10: In Exercises 1015, give lim x f(x) and lim x+ f(x)
 1.8.11: In Exercises 1015, give lim x f(x) and lim x+ f(x)
 1.8.12: In Exercises 1015, give lim x f(x) and lim x+ f(x)
 1.8.13: In Exercises 1015, give lim x f(x) and lim x+ f(x)
 1.8.14: In Exercises 1015, give lim x f(x) and lim x+ f(x)
 1.8.15: In Exercises 1015, give lim x f(x) and lim x+ f(x)
 1.8.16: Estimate the limits in Exercises 1617 graphically.
 1.8.17: Estimate the limits in Exercises 1617 graphically.
 1.8.18: Does f(x) = x x have right or left limits at 0? Is f(x) continuous?
 1.8.19: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.20: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.21: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.22: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.23: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.24: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.25: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.26: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.27: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.28: Use a graph to estimate each of the limits in Exercises 1928. Use r...
 1.8.29: For the functions in Exercises 2931, use algebra to evaluate the li...
 1.8.30: For the functions in Exercises 2931, use algebra to evaluate the li...
 1.8.31: For the functions in Exercises 2931, use algebra to evaluate the li...
 1.8.32: Estimate how close should be to 0 to make (sin )/ stay within 0.001...
 1.8.33: Write the definition of the following statement both in words and i...
 1.8.34: In 3437, is the function continuous for all x? If not, say where it...
 1.8.35: In 3437, is the function continuous for all x? If not, say where it...
 1.8.36: In 3437, is the function continuous for all x? If not, say where it...
 1.8.37: In 3437, is the function continuous for all x? If not, say where it...
 1.8.38: By graphing y = (1 + x) 1/x, estimate lim x0 (1 + x) 1/x. You shoul...
 1.8.39: Investigate lim h0 (1 + h) 1/h numerically.
 1.8.40: Investigate lim h0 (1 + h) 1/h numerically.
 1.8.41: If p(x)is the function on page 54 giving the price of mailing a fir...
 1.8.42: The notation limx0+ means that we only consider values of x greater...
 1.8.43: In 4345, modify the definition of limit on page 59 to give a defini...
 1.8.44: In 4345, modify the definition of limit on page 59 to give a defini...
 1.8.45: In 4345, modify the definition of limit on page 59 to give a defini...
 1.8.46: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.47: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.48: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.49: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.50: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.51: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.52: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.53: For the functions in 4653, do the following: (a) Make a table of va...
 1.8.54: Assuming that limits as x have the properties listed for limits as ...
 1.8.55: Assuming that limits as x have the properties listed for limits as ...
 1.8.56: Assuming that limits as x have the properties listed for limits as ...
 1.8.57: Assuming that limits as x have the properties listed for limits as ...
 1.8.58: Assuming that limits as x have the properties listed for limits as ...
 1.8.59: Assuming that limits as x have the properties listed for limits as ...
 1.8.60: Assuming that limits as x have the properties listed for limits as ...
 1.8.61: Assuming that limits as x have the properties listed for limits as ...
 1.8.62: Assuming that limits as x have the properties listed for limits as ...
 1.8.63: Assuming that limits as x have the properties listed for limits as ...
 1.8.64: In 6471, find a value of the constant k such that the limit exists.
 1.8.65: In 6471, find a value of the constant k such that the limit exists.
 1.8.66: In 6471, find a value of the constant k such that the limit exists.
 1.8.67: In 6471, find a value of the constant k such that the limit exists.
 1.8.68: In 6471, find a value of the constant k such that the limit exists.
 1.8.69: In 6471, find a value of the constant k such that the limit exists.
 1.8.70: In 6471, find a value of the constant k such that the limit exists.
 1.8.71: In 6471, find a value of the constant k such that the limit exists.
 1.8.72: For each value of in 7273, find a positive value of such that the g...
 1.8.73: For each value of in 7273, find a positive value of such that the g...
 1.8.74: Show that lim x0 (2x + 3) = 3. [Hint: Use 72.]
 1.8.75: Consider the function f(x) = sin(1/x). (a) Find a sequence of xval...
 1.8.76: For the functions in 7677, do the following: (a) Make a table of va...
 1.8.77: For the functions in 7677, do the following: (a) Make a table of va...
 1.8.78: This problem suggests a proof of the first property of limits on pa...
 1.8.79: Prove the second property of limits: lim xc (f(x) + g(x)) = lim xc ...
 1.8.80: This problem suggests a proof of the third property of limits (assu...
 1.8.81: Show f(x) = x is continuous everywhere.
 1.8.82: Use to show that for any positive integer n, the function xn is con...
 1.8.83: Use Theorem 1.2 on page 60 to explain why if f and g are continuous...
 1.8.84: In 8486, explain what is wrong with the statement.
 1.8.85: In 8486, explain what is wrong with the statement.
 1.8.86: In 8486, explain what is wrong with the statement.
 1.8.87: In 8788, give an example of:
 1.8.88: In 8788, give an example of:
 1.8.89: Suppose that limx3 f(x)=7. Are the statements in 8995 true or false...
 1.8.90: Suppose that limx3 f(x)=7. Are the statements in 8995 true or false...
 1.8.91: Suppose that limx3 f(x)=7. Are the statements in 8995 true or false...
 1.8.92: Suppose that limx3 f(x)=7. Are the statements in 8995 true or false...
 1.8.93: Suppose that limx3 f(x)=7. Are the statements in 8995 true or false...
 1.8.94: Suppose that limx3 f(x)=7. Are the statements in 8995 true or false...
 1.8.95: Suppose that limx3 f(x)=7. Are the statements in 8995 true or false...
 1.8.96: Which of the statements in 96100 are true about every function f(x)...
 1.8.97: Which of the statements in 96100 are true about every function f(x)...
 1.8.98: Which of the statements in 96100 are true about every function f(x)...
 1.8.99: Which of the statements in 96100 are true about every function f(x)...
 1.8.100: Which of the statements in 96100 are true about every function f(x)...
 1.8.101: Which of the statements in 96100 are true about every function f(x)...
Solutions for Chapter 1.8: LIMITS
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 1.8: LIMITS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.8: LIMITS includes 101 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. Since 101 problems in chapter 1.8: LIMITS have been answered, more than 34887 students have viewed full stepbystep solutions from this chapter.

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Focus, foci
See Ellipse, Hyperbola, Parabola.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Length of a vector
See Magnitude of a vector.

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

Monomial function
A polynomial with exactly one term.

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Relation
A set of ordered pairs of real numbers.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Terminal point
See Arrow.

Transformation
A function that maps real numbers to real numbers.

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Vertices of an ellipse
The points where the ellipse intersects its focal axis.

Zero factorial
See n factorial.