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Math Calculus CALCULUS

Making a Function Continuous In Exercises 59–64. find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. f ( x ) = { 2 , x ≤ − 1 a x + b , − 1 < x < 3 − 2 x ≥ 3

Making a Function Continuous In Exercises 59–64. find the constant a, or the constants a and b, such that the function is continuous on the entire real number line. f ( x ) = { 2 , x ≤ − 1 a x + b , − 1 < x < 3 − 2 x ≥ 3

Solution Summary: The author explains how to calculate the values of "a" and "b" for which the given function f(x) is continuous.

CALCULUS

11th Edition

ISBN: 9781337761512

Author: Larson

Publisher: CENGAGE L

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Chapter 1.4, Problem 63E

Making a Function Continuous In Exercises 59–64. find the constant a, or the constants a and b, such that the function is continuous on the entire real number line.

f ( x ) = { 2 , x ≤ − 1 a x + b , − 1 < x < 3 − 2 x ≥ 3

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Chapter 1.4, Problem 62E

Chapter 1.4, Problem 64E

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Chapter 1 Solutions

CALCULUS

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Use the graph of f to identify...Ch. 1.2 - Prob. 73E Ch. 1.2 - Prob. 74E Ch. 1.2 - Prob. 75E Ch. 1.2 - Prob. 76E Ch. 1.2 - Prob. 77E Ch. 1.2 - Prob. 78E Ch. 1.2 - Evaluating Limits Use a graphing utility to...Ch. 1.2 - Prob. 80E Ch. 1.2 - Proof Prove that if the limit of f(x) as x...Ch. 1.2 - Prob. 82E Ch. 1.2 - Prob. 83E Ch. 1.2 - Prob. 84E Ch. 1.2 - Inscribe a rectangle of base b and height h in a...Ch. 1.2 - Prob. 86E Ch. 1.2 - Estimating a Limit Numerically In Exercises 5-10,...Ch. 1.2 - Estimating a Limit Numerically In Exercises 5-10,...Ch. 1.3 - CONCEPT CHECK Polynomial Function Describe how to...Ch. 1.3 - Prob. 2E Ch. 1.3 - Squeeze Theorem In your own words, explain the...Ch. 1.3 - Prob. 4E Ch. 1.3 - Prob. 5E Ch. 1.3 - Finding a Limit In Exercises 5-22. find the limit....Ch. 1.3 - Prob. 7E Ch. 1.3 - Finding a Limit In Exercises 5-22. find the limit....Ch. 1.3 - Prob. 9E Ch. 1.3 - Prob. 12E Ch. 1.3 - Prob. 13E Ch. 1.3 - Prob. 14E Ch. 1.3 - Prob. 11E Ch. 1.3 - Prob. 10E Ch. 1.3 - Prob. 15E Ch. 1.3 - Finding a Limit In Exercises 5-22, find the limit....Ch. 1.3 - Prob. 17E Ch. 1.3 - Prob. 18E Ch. 1.3 - Prob. 19E Ch. 1.3 - Prob. 20E Ch. 1.3 - Prob. 21E Ch. 1.3 - Finding a Limit In Exercises 5-22, find the limit....Ch. 1.3 - Finding Limits In Exercises 23-26, Find the...Ch. 1.3 - Finding Limits In Exercises 23-26, Find the...Ch. 1.3 - Finding Limits In Exercises 23-26, Find the...Ch. 1.3 - Prob. 26E Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 28E Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 32E Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 34E Ch. 1.3 - Prob. 35E Ch. 1.3 - Prob. 36E Ch. 1.3 - Prob. 37E Ch. 1.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 1.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 1.3 - Evaluating Limits In Exercises 37-40, use the...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Finding a Limit In Exercises 41-46, write a...Ch. 1.3 - Prob. 47E Ch. 1.3 - Prob. 48E Ch. 1.3 - Finding a Limit In Exercises 4762, find the limit....Ch. 1.3 - Finding a Limit In Exercises 4762, find the limit....Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Prob. 55E Ch. 1.3 - Prob. 56E Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Prob. 58E Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Prob. 61E Ch. 1.3 - Finding a Limit In Exercises 47-62, find the...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 71E Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 73E Ch. 1.3 - Finding a Limit of a Trigonometric Function In...Ch. 1.3 - Prob. 75E Ch. 1.3 - Prob. 76E Ch. 1.3 - Prob. 77E Ch. 1.3 - Prob. 78E Ch. 1.3 - Prob. 79E Ch. 1.3 - Prob. 80E Ch. 1.3 - Prob. 81E Ch. 1.3 - Prob. 82E Ch. 1.3 - Prob. 83E Ch. 1.3 - Finding a Limit In Exercises 83-90, find...Ch. 1.3 - Prob. 85E Ch. 1.3 - Finding a Limit In Exercises 83-90, find...Ch. 1.3 - Prob. 87E Ch. 1.3 - Prob. 88E Ch. 1.3 - Prob. 89E Ch. 1.3 - Prob. 90E Ch. 1.3 - Using the Squeeze Theorem In Exercises 91 and 92,...Ch. 1.3 - Using the Squeeze Theorem In Exercises 91 and 92,...Ch. 1.3 - Using the Squeeze Theorem In Exercises 93-96, use...Ch. 1.3 - Using the Squeeze Theorem In Exercises 93-96, use...Ch. 1.3 - Prob. 95E Ch. 1.3 - Prob. 96E Ch. 1.3 - Functions That Agree at All but One Point (a) In...Ch. 1.3 - Prob. 98E Ch. 1.3 - Prob. 99E Ch. 1.3 - HOW DO YOU SEE IT? Would you use the dividing out...Ch. 1.3 - Prob. 101E Ch. 1.3 - Free-Falling Object In Exercises 101 and 102. use...Ch. 1.3 - Free-Falling Object In Exercises 103 and 104, use...Ch. 1.3 - Free-Falling Object In Exercises 103 and 104, use...Ch. 1.3 - Prob. 105E Ch. 1.3 - Prob. 106E Ch. 1.3 - Proof Prove Property 1 of Theorem 1.1.Ch. 1.3 - Proof Prove Property 3 of Theorem 1.1. (You may...Ch. 1.3 - Proof Prove Property 1 of Theorem 1.2.Ch. 1.3 - Prob. 110E Ch. 1.3 - Prob. 111E Ch. 1.3 - Prob. 112E Ch. 1.3 - Prob. 113E Ch. 1.3 - Prob. 114E Ch. 1.3 - Prob. 115E Ch. 1.3 - Prob. 116E Ch. 1.3 - Prob. 117E Ch. 1.3 - True or False? In Exercises 115-120, determine...Ch. 1.3 - Prob. 119E Ch. 1.3 - Prob. 120E Ch. 1.3 - Prob. 121E Ch. 1.3 - Piecewise Functions Let...Ch. 1.3 - Graphical Reasoning Consider f(x)=secx1x2. (a)...Ch. 1.3 - Approximation (a) Find limx01cosxx2. (b) Use your...Ch. 1.4 - CONCEPT CHECK Continuity In your own words,...Ch. 1.4 - Prob. 2E Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 1.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 1.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 1.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 1.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 1.4 - Limits and Continuity In Exercises 5-10, use the...Ch. 1.4 - Prob. 11E Ch. 1.4 - Prob. 12E Ch. 1.4 - Prob. 13E Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Prob. 17E Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Prob. 21E Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Finding a Limit In Exercises 11-30, find the limit...Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Continuity of a Function In Exercises 31-34,...Ch. 1.4 - Continuity of a Function In Exercises 31-34,...Ch. 1.4 - Continuity of a Function In Exercises 31-34,...Ch. 1.4 - Continuity of a Function In Exercises 31-34,...Ch. 1.4 - Continuity on a Closed Interval In Exercises...Ch. 1.4 - Continuity on a Closed Interval In Exercises...Ch. 1.4 - Continuity on a Closed Interval In Exercises...Ch. 1.4 - Continuity on a Closed Interval In Exercises...Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Prob. 40E Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Prob. 42E Ch. 1.4 - Prob. 43E Ch. 1.4 - Prob. 44E Ch. 1.4 - Prob. 45E Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Prob. 49E Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Prob. 53E Ch. 1.4 - Removable and Nonremovable Discontinuities In...Ch. 1.4 - Prob. 55E Ch. 1.4 - Prob. 56E Ch. 1.4 - Prob. 57E Ch. 1.4 - Prob. 58E Ch. 1.4 - Prob. 59E Ch. 1.4 - Making a Function Continuous In Exercises 59-64,...Ch. 1.4 - Making a Function Continuous In Exercises 59-64,...Ch. 1.4 - Making a Function Continuous In Exercises 59-64,...Ch. 1.4 - Making a Function Continuous In Exercises 5964....Ch. 1.4 - Making a Function Continuous In Exercises 59-64,...Ch. 1.4 - Prob. 65E Ch. 1.4 - Prob. 66E Ch. 1.4 - Prob. 67E Ch. 1.4 - Prob. 68E Ch. 1.4 - Continuity of a Composite Function In Exercises...Ch. 1.4 - Prob. 70E Ch. 1.4 - Prob. 71E Ch. 1.4 - Prob. 72E Ch. 1.4 - Prob. 73E Ch. 1.4 - Prob. 74E Ch. 1.4 - Prob. 75E Ch. 1.4 - Prob. 76E Ch. 1.4 - Prob. 77E Ch. 1.4 - Testing for Continuity In Exercises 75-82,...Ch. 1.4 - Prob. 79E Ch. 1.4 - Testing for Continuity In Exercises 75-82,...Ch. 1.4 - Prob. 81E Ch. 1.4 - Prob. 82E Ch. 1.4 - Prob. 83E Ch. 1.4 - Existence of a Zero In Exercises 83-86, explain...Ch. 1.4 - Existence of a Zero In Exercises 83-86, explain...Ch. 1.4 - Existence of a Zero In Exercises 83-86, explain...Ch. 1.4 - Prob. 87E Ch. 1.4 - Prob. 88E Ch. 1.4 - Prob. 89E Ch. 1.4 - Using the Intermediate Value Theorem In Exercises...Ch. 1.4 - Prob. 91E Ch. 1.4 - Prob. 92E Ch. 1.4 - Prob. 93E Ch. 1.4 - Prob. 94E Ch. 1.4 - Using the Intermediate Value Theorem In Exercises...Ch. 1.4 - Using the Intermediate Value Theorem In Exercises...Ch. 1.4 - Prob. 97E Ch. 1.4 - Prob. 98E Ch. 1.4 - Prob. 99E Ch. 1.4 - Prob. 100E Ch. 1.4 - Prob. 101E Ch. 1.4 - Prob. 102E Ch. 1.4 - Prob. 103E Ch. 1.4 - Prob. 104E Ch. 1.4 - Prob. 105E Ch. 1.4 - Prob. 106E Ch. 1.4 - Prob. 107E Ch. 1.4 - True or False? In Exercises 105-110. determine...Ch. 1.4 - True or False? In Exercises 105-110. determine...Ch. 1.4 - Prob. 110E Ch. 1.4 - Prob. 111E Ch. 1.4 - HOW DO YOU SEE IT? Every day you dissolve 28...Ch. 1.4 - Prob. 113E Ch. 1.4 - Prob. 114E Ch. 1.4 - Dj Vu At 8:00 a.m. on Saturday, a nun begins...Ch. 1.4 - Volume Use the Intermediate Value Theorem to show...Ch. 1.4 - Prob. 117E Ch. 1.4 - Prob. 118E Ch. 1.4 - Prob. 119E Ch. 1.4 - Signum Function The signum function is defined by...Ch. 1.4 - Prob. 121E Ch. 1.4 - Creating Models A swimmer crosses a pool of width...Ch. 1.4 - Making a Function Continuous Find all values of c...Ch. 1.4 - Prob. 124E Ch. 1.4 - Prob. 125E Ch. 1.4 - Prob. 126E Ch. 1.4 - Prob. 127E Ch. 1.4 - Prob. 128E Ch. 1.4 - Prob. 129E Ch. 1.4 - Prob. 130E Ch. 1.5 - Infinite Limit In your own words, describe the...Ch. 1.5 - Prob. 2E Ch. 1.5 - Determining Infinite Limits from a Graph In...Ch. 1.5 - Determining Infinite Limits from a Graph In...Ch. 1.5 - Determining Infinite Limits from a Graph In...Ch. 1.5 - Prob. 6E Ch. 1.5 - Prob. 7E Ch. 1.5 - Determining Infinite Limits from a Graph In...Ch. 1.5 - Determining Infinite Limits from a Graph In...Ch. 1.5 - Determining Infinite Limits from a Graph In...Ch. 1.5 - Numerical and Graphical Analysis In Exercises...Ch. 1.5 - Numerical and Graphical Analysis In Exercises...Ch. 1.5 - Prob. 13E Ch. 1.5 - Prob. 14E Ch. 1.5 - Prob. 15E Ch. 1.5 - Prob. 16E Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Prob. 18E Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Prob. 20E Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Prob. 22E Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Prob. 24E Ch. 1.5 - Prob. 25E Ch. 1.5 - Prob. 26E Ch. 1.5 - Prob. 27E Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Prob. 30E Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Finding Vertical Asymptotes In Exercises 17-32....Ch. 1.5 - Prob. 33E Ch. 1.5 - Prob. 34E Ch. 1.5 - Prob. 35E Ch. 1.5 - Prob. 36E Ch. 1.5 - Finding a One-Sided Limit In Exercises 37-50, find...Ch. 1.5 - Prob. 38E Ch. 1.5 - Finding a One-Sided Limit In Exercises 37-50, find...Ch. 1.5 - Prob. 40E Ch. 1.5 - Prob. 41E Ch. 1.5 - Prob. 42E Ch. 1.5 - Finding a One-Sided Limit In Exercises 37-50, find...Ch. 1.5 - Finding a One-Sided Limit In Exercises 37-50, find...Ch. 1.5 - Prob. 45E Ch. 1.5 - Finding a One-Sided Limit In Exercises 37-50, find...Ch. 1.5 - Prob. 47E Ch. 1.5 - Prob. 48E Ch. 1.5 - Prob. 49E Ch. 1.5 - Prob. 50E Ch. 1.5 - Prob. 51E Ch. 1.5 - Prob. 52E Ch. 1.5 - Prob. 53E Ch. 1.5 - Prob. 54E Ch. 1.5 - Prob. 55E Ch. 1.5 - Prob. 56E Ch. 1.5 - Prob. 57E Ch. 1.5 - Relativity According to the theory of relativity,...Ch. 1.5 - Prob. 59E Ch. 1.5 - Prob. 60E Ch. 1.5 - Rate of Change A 25-foot ladder is leaning against...Ch. 1.5 - Average Speed On a trip of d miles to another...Ch. 1.5 - Numerical and Graphical Analysis Consider the...Ch. 1.5 - Numerical and Graphical Reasoning A crossed belt...Ch. 1.5 - Prob. 65E Ch. 1.5 - True or False? In Exercises 65-68, determine...Ch. 1.5 - True or False? In Exercises 65-68, determine...Ch. 1.5 - Prob. 68E Ch. 1.5 - Finding Functions Find functions f and g such that...Ch. 1.5 - Prob. 70E Ch. 1.5 - Prob. 71E Ch. 1.5 - Prob. 72E Ch. 1.5 - Prob. 73E Ch. 1.5 - Prob. 74E Ch. 1.5 - Prob. 75E Ch. 1.5 - Prob. 76E Ch. 1 - Precalculus or Calculus In Exercises 1 and 2,...Ch. 1 - Precalculus or Calculus In Exercises 1 and 2,...Ch. 1 - Prob. 3RE Ch. 1 - Estimating a Limit Numerically In Exercises 3 and...Ch. 1 - Prob. 5RE Ch. 1 - Prob. 6RE Ch. 1 - Using the Definition of a Limit In Exercises 710,...Ch. 1 - Prob. 8RE Ch. 1 - Prob. 9RE Ch. 1 - Prob. 10RE Ch. 1 - Finding a Limit In Exercises 11-28, find the...Ch. 1 - Finding a Limit In Exercises 11-28, Find the...Ch. 1 - Prob. 13RE Ch. 1 - Prob. 15RE Ch. 1 - Prob. 14RE Ch. 1 - Prob. 16RE Ch. 1 - Prob. 17RE Ch. 1 - Prob. 18RE Ch. 1 - Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - Prob. 21RE Ch. 1 - Prob. 22RE Ch. 1 - Prob. 23RE Ch. 1 - Prob. 24RE Ch. 1 - Finding a Limit In Exercises 1128, find the limit....Ch. 1 - Prob. 26RE Ch. 1 - Prob. 27RE Ch. 1 - Prob. 28RE Ch. 1 - Prob. 29RE Ch. 1 - Prob. 30RE Ch. 1 - Prob. 31RE Ch. 1 - Evaluating a Limit In Exercises 29-32, evaluate...Ch. 1 - Prob. 33RE Ch. 1 - Graphical, Numerical, and Analytic Analysis In...Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Free-Falling Object In Exercises 37 and 38. use...Ch. 1 - Free-Falling Object In Exercises 37 and 38. use...Ch. 1 - Prob. 39RE Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Finding a Limit In Exercises 39-50, find the limit...Ch. 1 - Finding a Limit In Exercises 39-50, find the limit...Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - Prob. 46RE Ch. 1 - Prob. 47RE Ch. 1 - Prob. 48RE Ch. 1 - Prob. 49RE Ch. 1 - Prob. 50RE Ch. 1 - Prob. 51RE Ch. 1 - Prob. 52RE Ch. 1 - Prob. 53RE Ch. 1 - Prob. 54RE Ch. 1 - Prob. 55RE Ch. 1 - Prob. 56RE Ch. 1 - Prob. 57RE Ch. 1 - Prob. 58RE Ch. 1 - Prob. 59RE Ch. 1 - Prob. 60RE Ch. 1 - Prob. 61RE Ch. 1 - Prob. 62RE Ch. 1 - Prob. 63RE Ch. 1 - Prob. 64RE Ch. 1 - Prob. 65RE Ch. 1 - Prob. 66RE Ch. 1 - Using the Intermediate Value Theorem Use the...Ch. 1 - Prob. 68RE Ch. 1 - Prob. 69RE Ch. 1 - Prob. 70RE Ch. 1 - Prob. 71RE Ch. 1 - Determining Infinite Limits In Exercises 71 and...Ch. 1 - Prob. 73RE Ch. 1 - Prob. 74RE Ch. 1 - Prob. 75RE Ch. 1 - Prob. 76RE Ch. 1 - Prob. 77RE Ch. 1 - Prob. 78RE Ch. 1 - Finding a One-Sided Limit In Exercises 79-88, find...Ch. 1 - Prob. 80RE Ch. 1 - Prob. 81RE Ch. 1 - Prob. 82RE Ch. 1 - Prob. 83RE Ch. 1 - Prob. 84RE Ch. 1 - Prob. 85RE Ch. 1 - Prob. 86RE Ch. 1 - Prob. 87RE Ch. 1 - Prob. 88RE Ch. 1 - Environment A utility company burns coal to...Ch. 1 - Perimeter Let P (x. y) be a point on the parabola...Ch. 1 - Area Let P(x, y) be a point on the parabola y=x2...Ch. 1 - Prob. 3PS Ch. 1 - Tangent Line Let P (3, 4) be a point on the circle...Ch. 1 - Tangent Line Let P(5,12) be a point on the circle...Ch. 1 - Finding Values Find the values of the constants a...Ch. 1 - Prob. 7PS Ch. 1 - Making a Function Continuous Find all values of...Ch. 1 - Choosing Graphs Consider the graphs of the four...Ch. 1 - Prob. 10PS Ch. 1 - Limits and Continuity Sketch the graph of the...Ch. 1 - Escape Velocity To escape Earth's gravitational...Ch. 1 - Pulse Function For positive numbers ab, the pulse...Ch. 1 - Proof Let a be a nonzero constant. 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