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6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

Chapter 2.5, Problem 37E

Textbook Problem

Finding a One-Sided Limit In Exercises 37–54, find the one-sided limit (if it exists).

Calculus: Early Transcendental Functions (MindTap Course List)

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Use the graph of f to identify...Ch. 2.2 - True or False? In Exercises 75-78, determine...Ch. 2.2 - True or False? In Exercises 75-78, determine...Ch. 2.2 - True or False? In Exercises 75-78, determine...Ch. 2.2 - True or False? In Exercises 75-78, determine...Ch. 2.2 - Determining a Limit In Exercises 79 and 80,...Ch. 2.2 - Determining a Limit In Exercises 79 and 80,...Ch. 2.2 - Evaluating Limits Use a graphing utility to...Ch. 2.2 - Evaluating Limits Use a graphing utility to...Ch. 2.2 - Proof Prove that if the limit of f (x) as x...Ch. 2.2 - Proof Consider the line f(x)=mx+b, where m0. 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Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit In Exercises 536, find the limit...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Evaluating Limits In Exercises 4144, use the...Ch. 2.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 2.3 - Evaluating Limits In Exercises 4144, use the...Ch. 2.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 2.3 - Finding a Limit In Exercises 41-46, write a...Ch. 2.3 - Finding a Limit In Exercises 41-46, write a...Ch. 2.3 - Finding a Limit In Exercises 41-46, write a...Ch. 2.3 - Finding a Limit In Exercises 41-46, write a...Ch. 2.3 - Finding a Limit In Exercises 41-46, write a...Ch. 2.3 - Finding a Limit In Exercises 41-46, write a...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 5166, find the limit....Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit In Exercises 47-62, find the...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Finding a Limit of a Transcendental Function In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Graphical, Numerical, and Analytic Analysis In...Ch. 2.3 - Finding a Limit In Exercises 87-94, find...Ch. 2.3 - Finding a Limit In Exercises 87-94, find...Ch. 2.3 - Finding a Limit In Exercises 87-94, find...Ch. 2.3 - Finding a Limit In Exercises 9194, find...Ch. 2.3 - Using the Squeeze Theorem In Exercises 95 and 96,...Ch. 2.3 - Using the Squeeze Theorem In Exercises 95 and 96,...Ch. 2.3 - Using the Squeeze Theorem In Exercises 97-100, use...Ch. 2.3 - Using the Squeeze Theorem In Exercises 97-100, use...Ch. 2.3 - Using the Squeeze Theorem In Exercises 97-100, use...Ch. 2.3 - Using the Squeeze Theorem In Exercises 97-100, use...Ch. 2.3 - Functions That Agree at All but One Point (a) In...Ch. 2.3 - Writing Use a graphing utility to graph...Ch. 2.3 - HOW DO YOU SEE IT? Would you use the dividing out...Ch. 2.3 - In Exercises 105 and 106, use the position...Ch. 2.3 - In Exercises 105 and 106, use the position...Ch. 2.3 - Writing Use a graphing utility to graph f(x) = x,...Ch. 2.3 - Free-Falling Object In Exercises 107 and 108, use...Ch. 2.3 - Free-Falling Object In Exercises 107 and 108, use...Ch. 2.3 - Finding Functions Find two functions f and g such...Ch. 2.3 - Proof Prove that if limxcf(x) exists and...Ch. 2.3 - Prove that limxcb=b, where b and c are real...Ch. 2.3 - Proof Prove Property 3 of Theorem 2.1. (You may...Ch. 2.3 - Proof Prove Property 1 of Theorem 2.2.Ch. 2.3 - Proof Prove that if limxcf(x)=0, then...Ch. 2.3 - Proof Prove that if limxcf(x)=0 and |g(x)|M for a...Ch. 2.3 - Proof (a) Prove that if limxc|f(x)|=0, then...Ch. 2.3 - Think About It Find a function f to show that the...Ch. 2.3 - Think About It When using a graphing utility to...Ch. 2.3 - True or False? In Exercises 119-124, determine...Ch. 2.3 - True or False? In Exercises 119-124, determine...Ch. 2.3 - True or False? In Exercises 119-124, determine...Ch. 2.3 - True or False? In Exercises 119-124, determine...Ch. 2.3 - True or False? In Exercises 119-124, determine...Ch. 2.3 - True or False? In Exercises 119-124, determine...Ch. 2.3 - Proof Prove the second part of Theorem 2.9....Ch. 2.3 - Piecewise Functions Let...Ch. 2.3 - Graphical Reasoning Consider f(x)secx1x2. (a) Find...Ch. 2.3 - Approximation (a) Find limx01cosxx2. (b) Use your...Ch. 2.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 2.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 2.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 2.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 2.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 2.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - Finding a Limit In Exercises 11-32, find the limit...Ch. 2.4 - 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Continuity on a Closed Interval In Exercises...Ch. 2.4 - Continuity on a Closed Interval In Exercises...Ch. 2.4 - Continuity on a Closed Interval In Exercises...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Removable and Nonremovable Discontinuities In...Ch. 2.4 - Making a Function Continuous In Exercises 61-66,...Ch. 2.4 - Making a Function Continuous In Exercises 61-66,...Ch. 2.4 - Making a Function Continuous In Exercises 61-66,...Ch. 2.4 - Making a Function Continuous In Exercises 6368,...Ch. 2.4 - Making a Function Continuous In Exercises 61-66,...Ch. 2.4 - Making a Function Continuous In Exercises 61-66,...Ch. 2.4 - Continuity of a Composite Function In Exercises...Ch. 2.4 - Continuity of a Composite Function In Exercises...Ch. 2.4 - Continuity of a Composite Function In Exercises...Ch. 2.4 - Continuity of a Composite Function In Exercises...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 7784, describe...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Writing In Exercises 8588, use a graphing utility...Ch. 2.4 - Writing In Exercises 8588, use a graphing utility...Ch. 2.4 - Writing In Exercises 8588, use a graphing utility...Ch. 2.4 - Writing In Exercises 8588, use a graphing utility...Ch. 2.4 - Existence of a Zero In Exercises 83-88, explain...Ch. 2.4 - Writing In Exercises 8992, explain why the...Ch. 2.4 - Existence of a Zero In Exercises 83-88, explain...Ch. 2.4 - Existence of a Zero In Exercises 83-88, explain...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Intermediate Value Theorem In Exercises...Ch. 2.4 - Using the Definition of Continuity State how...Ch. 2.4 - Sketching a Graph Sketch the graph of any function...Ch. 2.4 - Continuity of Combinations of Functions If the...Ch. 2.4 - Removable and Nonremovable Discontinuities...Ch. 2.4 - True or False? In Exercises 109-114, determine...Ch. 2.4 - True or False? In Exercises 109-114, determine...Ch. 2.4 - True or False? In Exercises 109-114, determine...Ch. 2.4 - True or False? In Exercises 109-114, determine...Ch. 2.4 - Think About It Describe how the functions...Ch. 2.4 - HOW DO YOU SEE IT? Every day you dissolve 28...Ch. 2.4 - Telephone Charges A long distance phone service...Ch. 2.4 - Inventory Management The number of units in...Ch. 2.4 - Dj Vu At 8:00 a.m. on Saturday, a man begins...Ch. 2.4 - Volume Use the Intermediate Value Theorem to show...Ch. 2.4 - Proof Prove that if f is continuous and has no...Ch. 2.4 - Dirichlet Function Show that the Dirichlet...Ch. 2.4 - Continuity of a Function Show that the function...Ch. 2.4 - Signum Function The signum function is defined by...Ch. 2.4 - Modeling Data The table lists the speeds S (in...Ch. 2.4 - Creating Models A swimmer crosses a pool of width...Ch. 2.4 - Making a Function Continuous Find all values of c...Ch. 2.4 - Proof Prove that for any real number y there...Ch. 2.4 - Making a Function Continuous Let f(x)=x+c2cx,c0....Ch. 2.4 - Proof Prove that if limx0f(c+x)=f(c) then f is...Ch. 2.4 - Continuity of a Function Discuss the continuity of...Ch. 2.4 - Proof (a) Let f1(x) and f2(x) be continuous on the...Ch. 2.4 - Prove or disprove: If x and y are real numbers...Ch. 2.4 - Determine all polynomials P(x) such that...Ch. 2.5 - Infinite Limit In your own words, describe the...Ch. 2.5 - Determining Infinite Limits from a Graph In...Ch. 2.5 - Determining Infinite Limits from a Graph In...Ch. 2.5 - Determining Infinite Limits from a Graph In...Ch. 2.5 - Determining Infinite Limits from a Graph In...Ch. 2.5 - Determining Infinite Limits In Exercises 7-10,...Ch. 2.5 - Determining Infinite Limits In Exercises 7-10,...Ch. 2.5 - Determining Infinite Limits In Exercises 7-10,...Ch. 2.5 - Determining Infinite Limits In Exercises 7-10,...Ch. 2.5 - Numerical and Graphical Analysis In Exercises...Ch. 2.5 - Numerical and Graphical Analysis In Exercises...Ch. 2.5 - Numerical and Graphical Analysis In Exercises...Ch. 2.5 - Numerical and Graphical Analysis In Exercises...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 1332,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 1332,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 1332,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 1332,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 1332,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 1332,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Finding Vertical Asymptotes In Exercises 17-32,...Ch. 2.5 - Vertical Asymptote or Removable Discontinuity In...Ch. 2.5 - Vertical Asymptote or Removable Discontinuity In...Ch. 2.5 - Vertical Asymptote or Removable Discontinuity In...Ch. 2.5 - Vertical Asymptote or Removable Discontinuity In...Ch. 2.5 - Finding a One-Sided Limit In Exercises 3754, find...Ch. 2.5 - Finding a One-Sided Limit In Exercises 3754, find...Ch. 2.5 - Finding a One-Sided Limit In Exercises 37-52, find...Ch. 2.5 - Finding a One-Sided Limit In Exercises 37-52, find...Ch. 2.5 - Finding a One-Sided Limit In Exercises 37-52, find...Ch. 2.5 - Finding a One-Sided Limit In Exercises 37-52, find...Ch. 2.5 - Finding a One-Sided Limit In Exercises37-52. 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For a quantity of gas at a...Ch. 2.5 - Rate of Change A 25-foot ladder is leaning against...Ch. 2.5 - Average Speed On a trip of d miles to another...Ch. 2.5 - Numerical and Graphical Analysis Consider the...Ch. 2.5 - Numerical and Graphical Reasoning A crossed belt...Ch. 2.5 - True or False? In Exercises 67-70, determine...Ch. 2.5 - True or False? In Exercises 67-70, determine...Ch. 2.5 - True or False? In Exercises 67-70, determine...Ch. 2.5 - True or False? In Exercises 67-70, determine...Ch. 2.5 - Finding Functions Find functions f and g such that...Ch. 2.5 - Proof Prove the difference, product, and quotient...Ch. 2.5 - True or False? 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Find each limit (if...Ch. 2 - Finding Limits For f(x)=x(x1), find (a) the domain...Ch. 2 - Finding Vertical Asymptotes In Exercises 75-82,...Ch. 2 - Finding Vertical Asymptotes In Exercises 75-82,...Ch. 2 - Finding Vertical Asymptotes In Exercises 75-82,...Ch. 2 - Finding Vertical Asymptotes In Exercises 75-82,...Ch. 2 - Finding Vertical Asymptotes In Exercises 6976,...Ch. 2 - Finding Vertical Asymptotes In Exercises 75-82,...Ch. 2 - Finding Vertical Asymptotes In Exercises 75-82,...Ch. 2 - Finding Vertical Asymptotes In Exercises 75-82,...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Finding a One-Sided Limit In Exercises 83-94, find...Ch. 2 - Environment A utility company burns coal to...Ch. 2 - Limits and Continuity The function f is defined as...Ch. 2 - Perimeter Let P(x, y) be a point on the parabola...Ch. 2 - Area Let P(x, y) be a point on the parabola y=x2...Ch. 2 - Area of a Circle (a) Find the area of a regular...Ch. 2 - Tangent Line Let P(3,4) be a point on the circle...Ch. 2 - Tangent Line Let P(5,12) be a point on the circle...Ch. 2 - Finding Values Find the values of the constants a...Ch. 2 - Finding Limits Consider the function...Ch. 2 - Making a Function Continuous Find all values of...Ch. 2 - Choosing Graphs Consider the graphs of the four...Ch. 2 - Limits and Continuity Sketch the graph of the...Ch. 2 - Limits and Continuity Sketch the graph of the...Ch. 2 - Escape Velocity To escape Earth's gravitational...Ch. 2 - Pulse Function For positive numbers ab, the pulse...Ch. 2 - Proof Let a be a nonzero constant. 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