Explanation Definition used: “A function f is continuous at a number a if lim x → a f ( x ) = f ( a ) ”. Theorem used: The functions such as “Polynomials, rational functions, root functions, trigonometric functions, inverse trigonometric functions, exponential functions and logarithmic functions” are continuous at every number in their domains. Proof: Consider the function f ( x ) = { sin x if x < π 4 cos x if x ≥ π 4 . Here, f ( x ) = sin x is defined on the interval ( − ∞ , π 4 ) . Since f ( x ) = sin x is a trigonometric function and by Theorem, it is continuous on its domain ( − ∞ , π 4 ) . Also, f ( x ) = cos x is defined on the interval ( π 4 , ∞ ) . Since f ( x ) = cos x is a trigonometric function and by Theorem, it is continuous on its domain ( π 4 , ∞ ) . Therefore, f ( x ) is continuous on the interval ( − ∞ , π 4 ) ∪ ( π 4 , ∞ ) . To show f ( x ) is continuous on ( − ∞ , ∞ ) , it is enough to show f ( x ) is continuous at x = π 4 . At x = π 4 , f ( x ) = cos x and substitute x = π 4 in f ( x ) = cos x as follows, f ( π 4 ) = cos ( π 4 ) = 1 2 Therefore, f ( π 4 ) = 1 2 is defined

8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Question

Chapter 1.8, Problem 40E

To determine

To show: The function f(x)={sinx if x<π4cosx if x≥π4 is continuous on (−∞,∞).

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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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The function f ( x ) = { sin x if x < π 4 cos x if x ≥ π 4 is continuous on ( − ∞ , ∞ ) .

Solution Summary: The author explains that the function f(x)=lmathrmsin

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To show: The function f(x)={sinx if x<π4cosx if x≥π4 is continuous on (−∞,∞).

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The function f ( x ) = { sin x if x &lt; π 4 cos x if x ≥ π 4 is continuous on ( − ∞ , ∞ ) .

Solution Summary: The author explains that the function f(x)=lmathrmsin

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To show: The function f(x)={sinx if x<π4cosx if x≥π4 is continuous on (−∞,∞).

Chapter 1 Solutions

The function f ( x ) = { sin x if x < π 4 cos x if x ≥ π 4 is continuous on ( − ∞ , ∞ ) .