8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Textbook Question

Chapter 1.1, Problem 44E

Evaluate f(−3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the function.

44. f ( x ) = { − 1 if x ≤ 1 7 − 2 x if x > 1

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Chapter 1.1, Problem 43E

Chapter 1.1, Problem 45E

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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. 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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. 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(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. 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Evaluate f (−3), f (0), and f (2) for the piecewise defined function . Then sketch the graph of the function. 44. f ( x ) = { − 1 if x ≤ 1 7 − 2 x if x > 1

Solution Summary: The author explains how to find the values of f(-3), if the value of x is less than 0, substitute 3 for it in the function.

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Evaluate f (−3), f (0), and f (2) for the piecewise defined function . Then sketch the graph of the function. 44. f ( x ) = { − 1 if x ≤ 1 7 − 2 x if x &gt; 1

Solution Summary: The author explains how to find the values of f(-3), if the value of x is less than 0, substitute 3 for it in the function.

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Chapter 1 Solutions

Evaluate f (−3), f (0), and f (2) for the piecewise defined function . Then sketch the graph of the function. 44. f ( x ) = { − 1 if x ≤ 1 7 − 2 x if x > 1