Explanation Given information: The function is f ( x ) = 3 x + 5 7 − x . Calculation: Consider the function. f ( x ) = 3 x + 5 7 − x The vertical asymptote is, lim x → 7 + f ( x ) = − ∞ lim x → 7 − f ( x ) = ∞ Hence, the vertical asymptotes is x = 7 . The horizontal asymptote is, lim x → ∞ f ( x ) = lim x → ∞ 3 x + 5 7 − x = lim x !

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 4.4, Problem 25PS

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To explain: The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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Chapter 4.4, Problem 24PS

Chapter 4.4, Problem 26PS

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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

Chapter 4 Solutions

Calculus

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The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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Chapter 4 Solutions