(a) Explanation Given information : The expression lim x → ∞ f ( x ) = 5 . The expression lim x → ∞ f ( x (b) To determine To define : The meaning of the expression lim x → − ∞ f ( x ) = 3 .

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Question

Chapter 2.2, Problem 1E

(a)

To determine

To define: The meaning of the expression limx→∞f(x)=5 .

(b)

To determine

To define: The meaning of the expression limx→−∞f(x)=3 .

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Chapter 2.1, Problem 9P

Chapter 2.2, Problem 2E

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Taylor Series Approximation Example- H.W More terms used implies better approximation f(x) 4 f(x) Zero order f(x + 1) = f(x;) First order f(x; + 1) = f(x;) + f'(x;)h 1.0 Second order 0.5 True f(x + 1) = f(x) + f'(x)h + ƒ"(x;) h2 2! f(x+1) 0 x; = 0 x+1 = 1 x h f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2 51 Taylor Series Approximation H.w: Smaller step size implies smaller error Errors f(x) + f(x,) Zero order f(x,+ 1) = f(x) First order 1.0 0.5 Reduced step size Second order True f(x + 1) = f(x) + f'(x)h f(x; + 1) = f(x) + f'(x)h + "(xi) h2 f(x,+1) O x₁ = 0 x+1=1 Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5 iterations (or & s= 5%) for f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2 52

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Chapter 2 Solutions

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The meaning of the expression lim x → ∞ f ( x ) = 5 .

Solution Summary: The author explains the meaning of the expression undersetxto -infty