 1.2.1: In Exercises 18, complete the table and use the result to estimate ...
 1.2.2: im x2 x 2 x 2 4 l
 1.2.3: lim x0 x 6 6 x
 1.2.4: lim x5 4 x 3 x 5 li
 1.2.5: lim x3 1 x 1 1 4 x 3 lim
 1.2.6: lim x4 x x 1 4 5 x 4 lim
 1.2.7: lim x0 sin x x
 1.2.8: lim x0 cos x 1 x
 1.2.9: In Exercises 914, create a table of values for the function and use...
 1.2.10: In Exercises 914, create a table of values for the function and use...
 1.2.11: In Exercises 914, create a table of values for the function and use...
 1.2.12: In Exercises 914, create a table of values for the function and use...
 1.2.13: In Exercises 914, create a table of values for the function and use...
 1.2.14: In Exercises 914, create a table of values for the function and use...
 1.2.15: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.16: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.17: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.18: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.19: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.20: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.21: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.22: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.23: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.24: In Exercises 1524, use the graph to find the limit (if it exists). ...
 1.2.25: In Exercises 25 and 26, use the graph of the function to decide whe...
 1.2.26: In Exercises 25 and 26, use the graph of the function to decide whe...
 1.2.27: In Exercises 27 and 28, use the graph of to identify the values of ...
 1.2.28: In Exercises 27 and 28, use the graph of to identify the values of ...
 1.2.29: In Exercises 29 and 30, sketch the graph of Then identify the value...
 1.2.30: fx sin x, 1 cos x, cos x, x < 0 0 x x > f
 1.2.31: In Exercises 31 and 32, sketch a graph of a function that satisfies...
 1.2.32: In Exercises 31 and 32, sketch a graph of a function that satisfies...
 1.2.33: For a long distance phone call, a hotel charges $9.99 for the first...
 1.2.34: Repeat Exercise 33 for Ct 5.79 0.99t 1. Ct
 1.2.35: The graph of is shown in the figure. Find such that if 0 < f x 3 < ...
 1.2.36: The graph of is shown in the figure. Find such that if then
 1.2.37: The graph of is shown in the figure. Find such that if then
 1.2.38: The graph of is shown in the figure. Find such that if then
 1.2.39: In Exercises 39 42, find the limit Then find such that whenever lim...
 1.2.40: lim x4 4 x 2
 1.2.41: lim x2 x 2 3
 1.2.42: lim x5 x 2 4
 1.2.43: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.44: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.45: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.46: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.47: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.48: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.49: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.50: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.51: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.52: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.53: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.54: In Exercises 4354, find the limit Then use the  definition to prov...
 1.2.55: What is the limit of as approaches r?
 1.2.56: What is the limit of as approaches r?
 1.2.57: In Exercises 5760, use a graphing utility to graph the function and...
 1.2.58: In Exercises 5760, use a graphing utility to graph the function and...
 1.2.59: In Exercises 5760, use a graphing utility to graph the function and...
 1.2.60: In Exercises 5760, use a graphing utility to graph the function and...
 1.2.61: Write a brief description of the meaning of the notation lim x8 fx 25.
 1.2.62: The definition of limit on page 52 requires that is a function defi...
 1.2.63: Identify three types of behavior associated with the nonexistence o...
 1.2.64: (a) If can you conclude anything about the limit of as approaches 2...
 1.2.65: A jeweler resizes a ring so that its inner circumference is 6 centi...
 1.2.66: A sporting goods manufacturer designs a golf ball having a volume o...
 1.2.67: Consider the function Estimate the limit by evaluating at values ne...
 1.2.68: Consider the function Estimate by evaluating at values near 0. Sket...
 1.2.69: The statement means that for each there corresponds a such that if ...
 1.2.70: The statement means that for each there corresponds a such that if ...
 1.2.71: In Exercises 7174, determine whether the statement is true or false...
 1.2.72: In Exercises 7174, determine whether the statement is true or false...
 1.2.73: In Exercises 7174, determine whether the statement is true or false...
 1.2.74: In Exercises 7174, determine whether the statement is true or false...
 1.2.75: Is a true statement? Explain.
 1.2.76: Is a true statement? Explain.
 1.2.77: Use a graphing utility to evaluate the limit for several values of ...
 1.2.78: Use a graphing utility to evaluate the limit for several values of ...
 1.2.79: Prove that if the limit of as exists, then the limit must be unique...
 1.2.80: Consider the line where Use the definition of limit to prove that l...
 1.2.81: Prove that is equivalent to lim xc fx L 0. xc
 1.2.82: (a) Given that prove that there exists an open interval containing ...
 1.2.83: Use the programming capabilities of a graphing utility to write a p...
 1.2.84: Use the program you created in Exercise 83 to approximate the limit...
 1.2.85: Inscribe a rectangle of base and height and an isosceles triangle o...
 1.2.86: A right circular cone has base of radius 1 and height 3. A cube is ...
Solutions for Chapter 1.2: Finding Limits Graphically and Numerically
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 1.2: Finding Limits Graphically and Numerically
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.2: Finding Limits Graphically and Numerically includes 86 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780547167022. Since 86 problems in chapter 1.2: Finding Limits Graphically and Numerically have been answered, more than 64108 students have viewed full stepbystep solutions from this chapter.

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

Acute triangle
A triangle in which all angles measure less than 90°

Base
See Exponential function, Logarithmic function, nth power of a.

Cosecant
The function y = csc x

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Doubleangle identity
An identity involving a trigonometric function of 2u

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Limit to growth
See Logistic growth function.

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Placebo
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

Right triangle
A triangle with a 90° angle.

Row operations
See Elementary row operations.

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Subtraction
a  b = a + (b)

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

Terminal point
See Arrow.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Xscl
The scale of the tick marks on the xaxis in a viewing window.