8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

Concept explainers

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

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Textbook Question

Chapter 1.8, Problem 21E

Explain why the function is discontinuous at the given number a. Sketch the graph of the function.

21. f ( x ) = { cos x if x < 0 0 if x = 0 1 − x 2 if x > 0 a = 0

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Chapter 1.8, Problem 20E

Chapter 1.8, Problem 22E

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Chapter 1 Solutions

Single Variable Calculus

Ch. 1.1 - If f(x)=x+2x and g(u)=u+2u, is it true that f = g?Ch. 1.1 - If f(x)=x2xx1andg(x)=x is it true that f = g?Ch. 1.1 - The graph of a function f is given. (a) State the...Ch. 1.1 - The graphs of f and g are given. (a) State the...Ch. 1.1 - Figure 1 was recorded by an instrument operated by...Ch. 1.1 - Prob. 6E Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Determine whether the curve is the graph of a...Ch. 1.1 - Prob. 10E

Ch. 1.1 - Shown is a graph of the global average temperature...Ch. 1.1 - Trees grow faster and form wider rings in warm...Ch. 1.1 - You put some ice cubes in a glass, fill the glass...Ch. 1.1 - Three runners compete in a 100-meter race. The...Ch. 1.1 - The graph shows the power consumption for a day in...Ch. 1.1 - Sketch a rough graph of the number of hours of...Ch. 1.1 - Prob. 17E Ch. 1.1 - Sketch a rough graph of the market value of a new...Ch. 1.1 - Sketch the graph of the amount of a particular...Ch. 1.1 - You place a frozen pie in an oven and bake it for...Ch. 1.1 - A homeowner mows the lawn every Wednesday...Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - If f(x) = 3x2 x + 2, find f(2), f(2), f(a), f(a),...Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Evaluate the difference quotient for the given...Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Find the domain of the function. 35. h(x)=1x25x4 Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Find the domain and range and sketch the graph of...Ch. 1.1 - Find the domain and sketch the graph of the...Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Evaluate f(3), f(0), and f(2) for the piecewise...Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Sketch the graph of the function. 48. h(t) = |t| +...Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Find an expression for the function whose graph is...Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.1 - Prob. 58E Ch. 1.1 - Prob. 59E Ch. 1.1 - Prob. 60E Ch. 1.1 - Prob. 61E Ch. 1.1 - A Norman window has the shape of a rectangle...Ch. 1.1 - A box with an open top is to be constructed from a...Ch. 1.1 - A cell phone plan has a basic charge of 35 a...Ch. 1.1 - Prob. 65E Ch. 1.1 - Prob. 66E Ch. 1.1 - In a certain country, income tax is assessed as...Ch. 1.1 - Prob. 68E Ch. 1.1 - Graphs of f and g are shown. Decide whether each...Ch. 1.1 - Graphs of f and g are shown. Decide whether each...Ch. 1.1 - Prob. 71E Ch. 1.1 - Prob. 72E Ch. 1.1 - Prob. 73E Ch. 1.1 - Prob. 74E Ch. 1.1 - Determine whether f is even, odd, or neither. If...Ch. 1.1 - Prob. 76E Ch. 1.1 - Prob. 77E Ch. 1.1 - Prob. 78E Ch. 1.1 - If f and g are both even functions, is f + g even?...Ch. 1.1 - Prob. 80E Ch. 1.2 - Classify each function as a power function, root...Ch. 1.2 - Classify each function as a power function, root...Ch. 1.2 - Prob. 3E Ch. 1.2 - Match each equation with its graph. Explain your...Ch. 1.2 - Prob. 5E Ch. 1.2 - Prob. 6E Ch. 1.2 - Prob. 7E Ch. 1.2 - Prob. 8E Ch. 1.2 - Prob. 9E Ch. 1.2 - Find expressions for the quadratic functions whose...Ch. 1.2 - Find an expression for a cubic function f if f(1)...Ch. 1.2 - Prob. 12E Ch. 1.2 - If the recommended adult dosage for a drug is D...Ch. 1.2 - The manager of a weekend flea market knows from...Ch. 1.2 - Prob. 15E Ch. 1.2 - Jason leaves Detroit at 2:00 pm and drives at a...Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - The monthly cost of driving a car depends on the...Ch. 1.2 - For each scatter plot, decide what type of...Ch. 1.2 - For each scatter plot, decide what type of...Ch. 1.3 - Suppose the graph of f is given. Write equations...Ch. 1.3 - Explain how each graph is obtained from the graph...Ch. 1.3 - The graph of y = f(x) is given. Match each...Ch. 1.3 - The graph of f is given. Draw the graphs of the...Ch. 1.3 - The graph of f is given. Use it to graph the...Ch. 1.3 - The graph of y=3xx2 is given. Use transformations...Ch. 1.3 - The graph of y=3xx2 is given. Use transformations...Ch. 1.3 - Prob. 8E Ch. 1.3 - Prob. 9E Ch. 1.3 - Prob. 10E Ch. 1.3 - Prob. 11E Ch. 1.3 - Prob. 12E Ch. 1.3 - Prob. 13E Ch. 1.3 - Prob. 14E Ch. 1.3 - Graph the function by hand, not by plotting...Ch. 1.3 - Prob. 16E 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 - Prob. 22E Ch. 1.3 - Prob. 23E Ch. 1.3 - Prob. 24E Ch. 1.3 - Prob. 25E Ch. 1.3 - A variable star is one whose brightness...Ch. 1.3 - Some of the highest tides in the world occur in...Ch. 1.3 - In a normal respiratory cycle the volume of air...Ch. 1.3 - Prob. 29E Ch. 1.3 - Use the given graph of f to sketch the graph of y...Ch. 1.3 - Prob. 31E Ch. 1.3 - Prob. 32E Ch. 1.3 - Prob. 33E Ch. 1.3 - Prob. 34E Ch. 1.3 - Prob. 35E Ch. 1.3 - Prob. 36E Ch. 1.3 - Prob. 37E Ch. 1.3 - Prob. 38E Ch. 1.3 - Prob. 39E Ch. 1.3 - Prob. 40E Ch. 1.3 - Prob. 41E Ch. 1.3 - Find f g h. 42. f(x) = tan x, g(x)=xx1,h(x)=x3 Ch. 1.3 - Prob. 43E Ch. 1.3 - Prob. 44E Ch. 1.3 - Prob. 45E Ch. 1.3 - Prob. 46E Ch. 1.3 - Express the function in the form f g. 47. v(t) =...Ch. 1.3 - Prob. 48E Ch. 1.3 - Prob. 49E Ch. 1.3 - Prob. 50E Ch. 1.3 - Express the function in the form f g h. 51. S(t)...Ch. 1.3 - Prob. 52E Ch. 1.3 - Use the given graphs of f and g to evaluate each...Ch. 1.3 - Use the given graphs of f and g to estimate the...Ch. 1.3 - A stone is dropped into a lake, creating a...Ch. 1.3 - Prob. 56E Ch. 1.3 - A ship is moving at a speed of 30 km/h parallel to...Ch. 1.3 - Prob. 58E Ch. 1.3 - The Heaviside function H is defined by...Ch. 1.3 - The Heaviside function defined in Exercise 59 can...Ch. 1.3 - Let f and g be linear functions with equations...Ch. 1.3 - Prob. 62E Ch. 1.3 - Prob. 63E Ch. 1.3 - Prob. 64E Ch. 1.3 - Prob. 65E Ch. 1.3 - Suppose g is an odd function and let h = f g. Is...Ch. 1.4 - A tank holds 1000 gallons of water, which drains...Ch. 1.4 - A cardiac monitor is used to measure the heart...Ch. 1.4 - The point P(2, 1) lies on the curve y = 1/(1 x)....Ch. 1.4 - The point P(0.5, 0) lies on the curve y = cos x....Ch. 1.4 - If a ball is thrown into the air with a velocity...Ch. 1.4 - If a rock is thrown upward on the planet Mars with...Ch. 1.4 - The table shows the position of a motorcyclist...Ch. 1.4 - The displacement (in centimeters) of a particle...Ch. 1.4 - The point P(1, 0) lies on the curve y = sin(10/x)....Ch. 1.5 - Prob. 1E Ch. 1.5 - Explain what it means to say that...Ch. 1.5 - Explain the meaning of each of the following. (a)...Ch. 1.5 - Use the given graph of f to state the value of...Ch. 1.5 - For the function f whose graph is given, state the...Ch. 1.5 - For the function h whose graph is given, state the...Ch. 1.5 - For the function g whose graph is given, state the...Ch. 1.5 - For the function A whose graph is shown, state the...Ch. 1.5 - For the function f whose graph is shown, state the...Ch. 1.5 - A patient receives a 150-mg injection of a drug...Ch. 1.5 - Sketch the graph of the function and use it to...Ch. 1.5 - Sketch the graph of the function and use it to...Ch. 1.5 - Use the graph of the function f to state the value...Ch. 1.5 - Use the graph of the function f to state the value...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Sketch the graph of an example of a function f...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Guess the value of the limit (if it exists) by...Ch. 1.5 - Prob. 23E Ch. 1.5 - Prob. 24E Ch. 1.5 - Use a table of values to estimate the value of the...Ch. 1.5 - Use a table of values to estimate the value of the...Ch. 1.5 - Prob. 27E Ch. 1.5 - Prob. 28E Ch. 1.5 - Determine the infinite limit. 29. limx5+x+1x5 Ch. 1.5 - Determine the infinite limit. 30. limx5x+1x5 Ch. 1.5 - Prob. 31E Ch. 1.5 - Determine the infinite limit. 32. limx3x(x3)5 Ch. 1.5 - Prob. 33E Ch. 1.5 - Prob. 34E Ch. 1.5 - Prob. 35E Ch. 1.5 - Prob. 36E Ch. 1.5 - Determine the infinite limit. 37. limx2xcscx Ch. 1.5 - Prob. 38E Ch. 1.5 - Determine the infinite limit. 39....Ch. 1.5 - Prob. 40E Ch. 1.5 - Determine limx11x31and limx1+1x31 (a) by...Ch. 1.5 - Prob. 42E Ch. 1.5 - (a) Evaluate the function f(x) = x2 (2x/1000) for...Ch. 1.5 - (a) Evaluate h(x) = (tan x x)/x3 for x = 1, 0.5,...Ch. 1.5 - Graph the function f(x) = sin(/x) of Example 4 in...Ch. 1.5 - Consider the function f(x)=tan1x. (a) Show that...Ch. 1.5 - Prob. 47E Ch. 1.5 - Prob. 48E Ch. 1.5 - (a) Use numerical and graphical evidence to guess...Ch. 1.6 - Given that limx2f(x)=4limx2g(x)=2limx2h(x)=0 find...Ch. 1.6 - The graphs of f and g are given. Use them to...Ch. 1.6 - Prob. 3E Ch. 1.6 - Prob. 4E Ch. 1.6 - Prob. 5E Ch. 1.6 - Prob. 6E Ch. 1.6 - Prob. 7E Ch. 1.6 - Evaluate the limit and justify each step by...Ch. 1.6 - Prob. 9E Ch. 1.6 - Prob. 10E Ch. 1.6 - Prob. 11E Ch. 1.6 - Prob. 12E Ch. 1.6 - Evaluate the limit, if it exists. 13....Ch. 1.6 - Prob. 14E Ch. 1.6 - Prob. 15E Ch. 1.6 - Prob. 16E Ch. 1.6 - Prob. 17E Ch. 1.6 - Prob. 18E Ch. 1.6 - Evaluate the limit, if it exists. 19. limx2x+2x3+8 Ch. 1.6 - Prob. 20E Ch. 1.6 - Prob. 21E Ch. 1.6 - Prob. 22E Ch. 1.6 - Prob. 23E Ch. 1.6 - Prob. 24E Ch. 1.6 - Evaluate the limit, if it exists. 25. limt01+t1tt Ch. 1.6 - Evaluate the limit, if it exists. 26....Ch. 1.6 - Prob. 27E Ch. 1.6 - Prob. 28E Ch. 1.6 - Prob. 29E Ch. 1.6 - Prob. 30E Ch. 1.6 - Evaluate the limit, if it exists. 31....Ch. 1.6 - Prob. 32E Ch. 1.6 - Prob. 33E Ch. 1.6 - Prob. 34E Ch. 1.6 - Use the Squeeze Theorem to show that limx0 (x2 cos...Ch. 1.6 - Prob. 36E Ch. 1.6 - Prob. 37E Ch. 1.6 - If 2x g(x) x4 x2 + 2 for all x, evaluate...Ch. 1.6 - Prob. 39E Ch. 1.6 - Prob. 40E Ch. 1.6 - Prob. 41E Ch. 1.6 - Prob. 42E Ch. 1.6 - Prob. 43E Ch. 1.6 - Prob. 44E Ch. 1.6 - Prob. 45E Ch. 1.6 - Prob. 46E Ch. 1.6 - The signum (or sign) function, denoted by sgn, is...Ch. 1.6 - Prob. 48E Ch. 1.6 - Prob. 49E Ch. 1.6 - Prob. 50E Ch. 1.6 - Let B(t)={412tift2t+cift2 Find the value of c so...Ch. 1.6 - Let g(x)={xifx13ifx=12x2if1x2x3ifx2 (a) Evaluate...Ch. 1.6 - Prob. 53E Ch. 1.6 - Let f(x) = cos x, x . (a) Sketch the graph of...Ch. 1.6 - If f(x) = x + x, show that limx2 f(x) exists but...Ch. 1.6 - Prob. 56E Ch. 1.6 - If p is a polynomial, show that limxa p(x) = p(a).Ch. 1.6 - If r is a rational function, use Exercise 57 to...Ch. 1.6 - If limx1f(x)8x1=10, find limx1f(x).Ch. 1.6 - Prob. 60E Ch. 1.6 - Prob. 61E Ch. 1.6 - Prob. 62E Ch. 1.6 - Show by means of an example that limxa [f(x) g(x)]...Ch. 1.6 - Prob. 64E Ch. 1.6 - Is there a number a such that limx23x2+ax+a+3x2+x2...Ch. 1.6 - Prob. 66E Ch. 1.7 - Use the given graph of f to find a number such...Ch. 1.7 - Prob. 2E Ch. 1.7 - Use the given graph of f(x)=x to find a number ...Ch. 1.7 - Use the given graph of f(x) = x2 to find a number ...Ch. 1.7 - Prob. 5E Ch. 1.7 - Prob. 6E Ch. 1.7 - For the limit limx2(x33x+4)=6 illustrate...Ch. 1.7 - Prob. 8E Ch. 1.7 - (a) Use a graph to find a number such that...Ch. 1.7 - Given that limxcsc2x=, illustrate Definition 6 by...Ch. 1.7 - Prob. 11E Ch. 1.7 - A crystal growth furnace is used in research to...Ch. 1.7 - Prob. 13E Ch. 1.7 - Given that limx2 (5x 7) = 3, illustrate...Ch. 1.7 - Prob. 15E Ch. 1.7 - Prob. 16E Ch. 1.7 - Prob. 17E Ch. 1.7 - Prob. 18E Ch. 1.7 - Prove the statement using the , definition of a...Ch. 1.7 - Prove the statement using the , definition of a...Ch. 1.7 - Prob. 21E Ch. 1.7 - Prob. 22E Ch. 1.7 - Prob. 23E Ch. 1.7 - Prob. 24E Ch. 1.7 - Prob. 25E Ch. 1.7 - Prob. 26E Ch. 1.7 - Prob. 27E Ch. 1.7 - Prob. 28E Ch. 1.7 - Prob. 29E Ch. 1.7 - Prob. 30E Ch. 1.7 - Prob. 31E Ch. 1.7 - Prob. 32E Ch. 1.7 - Prob. 33E Ch. 1.7 - Prob. 34E Ch. 1.7 - Prob. 36E Ch. 1.7 - Prove that limxax=a if a 0. [Hint:Usexa=xax+a.]Ch. 1.7 - Prob. 38E Ch. 1.7 - Prob. 39E Ch. 1.7 - Prob. 40E Ch. 1.7 - Prob. 41E Ch. 1.7 - Prob. 42E Ch. 1.7 - Prob. 43E Ch. 1.7 - Prob. 44E Ch. 1.8 - Write an equation that expresses the fact that a...Ch. 1.8 - If f is continuous on (, ), what can you say about...Ch. 1.8 - (a) From the graph of f, state the numbers at...Ch. 1.8 - From the graph of g, state the intervals on which...Ch. 1.8 - Sketch the graph of a function f that is...Ch. 1.8 - Prob. 6E Ch. 1.8 - Sketch the graph of a function f that is...Ch. 1.8 - Prob. 8E Ch. 1.8 - The toll T charged for driving on a certain...Ch. 1.8 - Prob. 10E Ch. 1.8 - Use the definition of continuity and the...Ch. 1.8 - Prob. 12E Ch. 1.8 - Prob. 13E Ch. 1.8 - Prob. 14E Ch. 1.8 - Use the definition of continuity and the...Ch. 1.8 - Prob. 16E Ch. 1.8 - Prob. 17E Ch. 1.8 - Prob. 18E Ch. 1.8 - Explain why the function is discontinuous at the...Ch. 1.8 - Prob. 20E Ch. 1.8 - Explain why the function is discontinuous at the...Ch. 1.8 - Prob. 22E Ch. 1.8 - Prob. 23E Ch. 1.8 - How would you remove the discontinuity of f? In...Ch. 1.8 - Prob. 25E Ch. 1.8 - Prob. 26E Ch. 1.8 - Explain, using Theorems 4, 5, 7, and 9, why the...Ch. 1.8 - Prob. 28E Ch. 1.8 - Prob. 29E Ch. 1.8 - Prob. 30E Ch. 1.8 - Prob. 31E Ch. 1.8 - Prob. 32E Ch. 1.8 - Locate the discontinuities of the function and...Ch. 1.8 - Prob. 34E Ch. 1.8 - Prob. 35E Ch. 1.8 - Prob. 36E Ch. 1.8 - Prob. 37E Ch. 1.8 - Prob. 38E Ch. 1.8 - Prob. 39E Ch. 1.8 - Prob. 40E Ch. 1.8 - Prob. 41E Ch. 1.8 - Find the numbers at which f is discontinuous. At...Ch. 1.8 - Find the numbers at which f is discontinuous. At...Ch. 1.8 - The gravitational force exerted by the planet...Ch. 1.8 - For what value of the constant c is the function f...Ch. 1.8 - Find the values of a and b that make f continuous...Ch. 1.8 - Suppose f and g are continuous functions such that...Ch. 1.8 - Prob. 48E Ch. 1.8 - Which of the following functions f has a removable...Ch. 1.8 - Suppose that a function f is continuous on [0, 1]...Ch. 1.8 - If f(x) = x2 + 10 sin x, show that there is a...Ch. 1.8 - Suppose f is continuous on [1, 5] and the only...Ch. 1.8 - Prob. 53E Ch. 1.8 - Use the Intermediate Value Theorem to show that...Ch. 1.8 - Prob. 55E Ch. 1.8 - Prob. 56E Ch. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - (a) Prove that the equation has at least one real...Ch. 1.8 - Prove, without graphing, that the graph of the...Ch. 1.8 - Prove, without graphing, that the graph of the...Ch. 1.8 - Prove that f is continuous at a if and only if...Ch. 1.8 - Prob. 64E Ch. 1.8 - Prob. 65E Ch. 1.8 - Prob. 66E Ch. 1.8 - Prob. 67E Ch. 1.8 - For what values of x is g continuous?...Ch. 1.8 - Prob. 69E Ch. 1.8 - If a and b are positive numbers, prove that the...Ch. 1.8 - Prob. 71E Ch. 1.8 - Prob. 72E Ch. 1.8 - A Tibetan monk leaves the monastery at 7:00 am and...Ch. 1 - (a) What is a function? What are its domain and...Ch. 1 - Prob. 2RCC Ch. 1 - Prob. 3RCC Ch. 1 - Prob. 4RCC Ch. 1 - Prob. 5RCC Ch. 1 - Prob. 6RCC Ch. 1 - Prob. 7RCC Ch. 1 - Draw, by hand, a rough sketch of the graph of each...Ch. 1 - Prob. 9RCC Ch. 1 - Prob. 10RCC Ch. 1 - Prob. 11RCC Ch. 1 - Prob. 12RCC Ch. 1 - Prob. 13RCC Ch. 1 - Prob. 14RCC Ch. 1 - Prob. 15RCC Ch. 1 - Prob. 16RCC Ch. 1 - Prob. 17RCC Ch. 1 - Prob. 18RCC Ch. 1 - Prob. 19RCC Ch. 1 - Prob. 1RQ Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 3RQ Ch. 1 - Prob. 4RQ Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 7RQ Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 9RQ Ch. 1 - Prob. 10RQ Ch. 1 - Prob. 11RQ Ch. 1 - Prob. 12RQ Ch. 1 - Prob. 13RQ Ch. 1 - Prob. 14RQ Ch. 1 - Prob. 15RQ Ch. 1 - Prob. 16RQ Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 18RQ Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 20RQ Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 22RQ Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Prob. 25RQ Ch. 1 - Prob. 26RQ Ch. 1 - Prob. 27RQ Ch. 1 - Let f be the function whose graph is given. (a)...Ch. 1 - Prob. 2RE Ch. 1 - Prob. 3RE Ch. 1 - Prob. 4RE Ch. 1 - Prob. 5RE Ch. 1 - Prob. 6RE Ch. 1 - Prob. 7RE Ch. 1 - Prob. 8RE Ch. 1 - Prob. 9RE Ch. 1 - The graph of f is given. Draw the graphs of the...Ch. 1 - Prob. 11RE Ch. 1 - Prob. 12RE Ch. 1 - Prob. 13RE Ch. 1 - Prob. 14RE Ch. 1 - Prob. 15RE Ch. 1 - Prob. 16RE Ch. 1 - Prob. 17RE Ch. 1 - Prob. 18RE Ch. 1 - Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - A small-appliance manufacturer finds that it costs...Ch. 1 - The graph of f is given. (a) Find each limit, or...Ch. 1 - Prob. 24RE Ch. 1 - Prob. 25RE 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 - Prob. 32RE Ch. 1 - Find the limit. 33. limu1u41u3+5u26u Ch. 1 - Find the limit. 34. limx3x+6xx33x2 Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Prob. 37RE Ch. 1 - Prob. 38RE Ch. 1 - If 2x 1 f(x) x2 for 0 x 3, find limx1 f(x).Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Prob. 42RE Ch. 1 - Prob. 43RE Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - Prob. 46RE Ch. 1 - Show that the function is continuous on its...Ch. 1 - Prob. 48RE Ch. 1 - Prob. 49RE Ch. 1 - Prob. 50RE Ch. 1 - Prob. 51RE Ch. 1 - Prob. 52RE Ch. 1 - Prob. 1P Ch. 1 - Prob. 2P Ch. 1 - Prob. 3P Ch. 1 - Prob. 4P Ch. 1 - Prob. 5P Ch. 1 - Prob. 6P Ch. 1 - The notation max{a, b, } means the largest of the...Ch. 1 - Prob. 8P Ch. 1 - Prob. 9P Ch. 1 - Prob. 10P Ch. 1 - Prove that if n is a positive integer, then 7n 1...Ch. 1 - Prob. 12P Ch. 1 - Prob. 13P Ch. 1 - Prob. 14P Ch. 1 - Prob. 15P Ch. 1 - Find numbers a and b such that limx0ax+b2x=1.Ch. 1 - Prob. 17P Ch. 1 - Prob. 18P Ch. 1 - Evaluate the following limits, if they exist,...Ch. 1 - Prob. 20P Ch. 1 - Prob. 21P Ch. 1 - A fixed point of a function f is a number c in its...Ch. 1 - Prob. 23P Ch. 1 - (a) The figure shows an isosceles triangle ABC...Ch. 1 - Prob. 25P

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Explain why the function is discontinuous at the given number a . Sketch the graph of the function. 21. f ( x ) = { cos x if x &lt; 0 0 if x = 0 1 − x 2 if x &gt; 0 a = 0

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Chapter 1 Solutions

Explain why the function is discontinuous at the given number a . Sketch the graph of the function. 21. f ( x ) = { cos x if x < 0 0 if x = 0 1 − x 2 if x > 0 a = 0