 1.3.1: In Exercises 14, use a graphing utility to graph the function and v...
 1.3.2: In Exercises 14, use a graphing utility to graph the function and v...
 1.3.3: In Exercises 14, use a graphing utility to graph the function and v...
 1.3.4: In Exercises 14, use a graphing utility to graph the function and v...
 1.3.5: In Exercises 522, find the limit.lim x2 x3
 1.3.6: In Exercises 522, find the limit.lim x2 x4 l
 1.3.7: In Exercises 522, find the limit.
 1.3.8: In Exercises 522, find the limit.
 1.3.9: In Exercises 522, find the limit.
 1.3.10: In Exercises 522, find the limit.
 1.3.11: In Exercises 522, find the limit.
 1.3.12: In Exercises 522, find the limit.
 1.3.13: In Exercises 522, find the limit.
 1.3.14: In Exercises 522, find the limit.lim x4 3 x 4
 1.3.15: In Exercises 522, find the limit.lim x4 x 32
 1.3.16: In Exercises 522, find the limit.lim x0 2x 13 l
 1.3.17: In Exercises 522, find the limit.lim x2 1 x
 1.3.18: In Exercises 522, find the limit.lim x3 2 x 2 l
 1.3.19: In Exercises 522, find the limit.
 1.3.20: In Exercises 522, find the limit.
 1.3.21: In Exercises 522, find the limit.
 1.3.22: In Exercises 522, find the limit.
 1.3.23: In Exercises 2326, find the limits. 23. (a) (b) (c)
 1.3.24: In Exercises 2326, find the limits. 23. (a) (b) (c)
 1.3.25: In Exercises 2326, find the limits. 23. (a) (b) (c)
 1.3.26: In Exercises 2326, find the limits. 23. (a) (b) (c)
 1.3.27: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.28: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.29: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.30: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.31: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.32: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.33: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.34: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.35: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.36: In Exercises 27 36, find the limit of the trigonometric function.
 1.3.37: In Exercises 3740, use the information to evaluate the limits.
 1.3.38: In Exercises 3740, use the information to evaluate the limits.
 1.3.39: In Exercises 3740, use the information to evaluate the limits.
 1.3.40: In Exercises 3740, use the information to evaluate the limits.
 1.3.41: In Exercises 4144, use the graph to determine the limit visually (i...
 1.3.42: In Exercises 4144, use the graph to determine the limit visually (i...
 1.3.43: In Exercises 4144, use the graph to determine the limit visually (i...
 1.3.44: In Exercises 4144, use the graph to determine the limit visually (i...
 1.3.45: lim x1 x 2 1 x 1 97
 1.3.46: lim x1 2x2 x 3 x 1
 1.3.47: lim x2 x 3 8 x 2 l
 1.3.48: lim x1 x3 1 x 1 l
 1.3.49: In Exercises 4964, find the limit (if it exists).limx0 x x2 x
 1.3.50: In Exercises 4964, find the limit (if it exists).limx0 3x x2 2x
 1.3.51: In Exercises 4964, find the limit (if it exists).lim x4 x 4 x2 16 l
 1.3.52: In Exercises 4964, find the limit (if it exists).lim x3 3 x x2 9
 1.3.53: In Exercises 4964, find the limit (if it exists).lim x3 x2 x 6 x2 9
 1.3.54: In Exercises 4964, find the limit (if it exists).lim x4 x2 5x 4 x2 ...
 1.3.55: In Exercises 4964, find the limit (if it exists).lim x4 x 5 3 x 4 l
 1.3.56: In Exercises 4964, find the limit (if it exists).lim x3 x 1 2 x 3 li
 1.3.57: In Exercises 4964, find the limit (if it exists).lim x0 x 5 5 x
 1.3.58: In Exercises 4964, find the limit (if it exists).lim x0 2 x 2 x l
 1.3.59: In Exercises 4964, find the limit (if it exists).lim x0 1 3 x 1 3 x
 1.3.60: In Exercises 4964, find the limit (if it exists).lim x0 1 x 4 1 4 x
 1.3.61: In Exercises 4964, find the limit (if it exists).lim x0 2x x 2x x
 1.3.62: In Exercises 4964, find the limit (if it exists).lim x0 x x2 x 2 x l
 1.3.63: In Exercises 4964, find the limit (if it exists).lim x0 x x2 2x x 1...
 1.3.64: In Exercises 4964, find the limit (if it exists).lim x0 x x3 x3 x
 1.3.65: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.66: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.67: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.68: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.69: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.70: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.71: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.72: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.73: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.74: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.75: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.76: In Exercises 6576, determine the limit of the trigonometric functio...
 1.3.77: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.78: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.79: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.80: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.81: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.82: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.83: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.84: In Exercises 7784, use a graphing utility to graph the function and...
 1.3.85: In Exercises 8588, find lim x0 fx 1 x fx x.fx 3x 2 l
 1.3.86: In Exercises 8588, find lim x0 fx 1 x fx x.fx x
 1.3.87: In Exercises 8588, find lim x0 fx 1 x fx x.fx 1 x 3
 1.3.88: In Exercises 8588, find lim x0 fx 1 x fx x.fx x2 4x f
 1.3.89: In Exercises 89 and 90, use the Squeeze Theorem to find lim xc fx.
 1.3.90: In Exercises 89 and 90, use the Squeeze Theorem to find lim xc fx.
 1.3.91: In Exercises 9196, use a graphing utility to graph the given functi...
 1.3.92: In Exercises 9196, use a graphing utility to graph the given functi...
 1.3.93: In Exercises 9196, use a graphing utility to graph the given functi...
 1.3.94: In Exercises 9196, use a graphing utility to graph the given functi...
 1.3.95: In Exercises 9196, use a graphing utility to graph the given functi...
 1.3.96: In Exercises 9196, use a graphing utility to graph the given functi...
 1.3.97: In the context of finding limits, discuss what is meant by two func...
 1.3.98: Give an example of two functions that agree at all but one point.
 1.3.99: What is meant by an indeterminate form?
 1.3.100: What is meant by an indeterminate form?
 1.3.101: Use a graphing utility to graph in the same viewing window. Compare...
 1.3.102: Use a graphing utility to graph in the same viewing window. Compare...
 1.3.103: In Exercises 103 and 104, use the position function which gives the...
 1.3.104: If a construction worker drops a wrench from a height of 500 feet, ...
 1.3.105: In Exercises 105 and 106, use the position function which gives the...
 1.3.106: Find the velocity of the object when t=3
 1.3.107: Find two functions and such that and do not exist, but does exist.
 1.3.108: Prove that if exists and does not exist, then does not exist.
 1.3.109: Prove Property 1 of Theorem 1.1.
 1.3.110: Prove Property 3 of Theorem 1.1. (You may use Property 3 of Theorem...
 1.3.111: Prove Property 1 of Theorem 1.2.
 1.3.112: Prove that if then lim xc fx 0. x
 1.3.113: Prove that if and for a fixed number and all then lim xc M x c, fxg...
 1.3.114: (a) Prove that if then (Note: This is the converse of Exercise 112....
 1.3.115: Find a function to show that the converse of Exercise 114(b) is not...
 1.3.116: In Exercises 117122, determine whether the statement is true or fal...
 1.3.117: In Exercises 117122, determine whether the statement is true or fal...
 1.3.118: In Exercises 117122, determine whether the statement is true or fal...
 1.3.119: In Exercises 117122, determine whether the statement is true or fal...
 1.3.120: In Exercises 117122, determine whether the statement is true or fal...
 1.3.121: In Exercises 117122, determine whether the statement is true or fal...
 1.3.122: In Exercises 117122, determine whether the statement is true or fal...
 1.3.123: Prove the second part of Theorem 1.9.lim x0 1 cos x x 0 l
 1.3.124: Let and Find (if possible) and
 1.3.125: Consider (a) Find the domain of (b) Use a graphing utility to graph...
 1.3.126: (a) Find (b) Use your answer to part (a) to derive the approximatio...
 1.3.127: When using a graphing utility to generate a table to approximate a ...
Solutions for Chapter 1.3: Evaluating Limits Analytically
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 1.3: Evaluating Limits Analytically
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780547167022. This textbook survival guide was created for the textbook: Calculus , edition: 9. Since 127 problems in chapter 1.3: Evaluating Limits Analytically have been answered, more than 67412 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.3: Evaluating Limits Analytically includes 127 full stepbystep solutions.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Average velocity
The change in position divided by the change in time.

Circular functions
Trigonometric functions when applied to real numbers are circular functions

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.

Descriptive statistics
The gathering and processing of numerical information

Differentiable at x = a
ƒ'(a) exists

Elimination method
A method of solving a system of linear equations

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

Equal matrices
Matrices that have the same order and equal corresponding elements.

Exponent
See nth power of a.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Focal length of a parabola
The directed distance from the vertex to the focus.

Measure of spread
A measure that tells how widely distributed data are.

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

Partial fraction decomposition
See Partial fractions.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Supply curve
p = ƒ(x), where x represents production and p represents price

Vertical component
See Component form of a vector.