Explanation Given: The derivative d d x ∫ 1 8 ln t d t . Concept Used: Second Fundamental Theorem of Calculus stats that if f is continuous on [ a , b ] and we define F ( x ) = ∫ a x f ( t ) d t for all x ∈ [ a , b ] , then F is continuous on [ a , b ] and differentiable on ( a , b ) . Fis antiderivative of f , that is, F ' ( x ) = f ( x ) . If f is continuous on [ a , b ] and u ( x ) is differentiable on [ a , b ] , then for all x ∈ [ a , b ] , d d x ∫ a u ( x )

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4.7, Problem 41S

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The derivative ddx∫18lnt dt using the Second Fundamental Theorem of Calculus.

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Chapter 4.7, Problem 40S

Chapter 4.7, Problem 42S

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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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Could you explain this using the formula I attached and polar coordinates

Chapter 4 Solutions

Calculus

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The derivative d d x ∫ 1 8 ln t d t using the Second Fundamental Theorem of Calculus.

Solution Summary: The author explains the second fundamental theorem of calculus, which states that if f is continuous on left[a,bright], then it's differentiable on

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The derivative ddx∫18lnt dt using the Second Fundamental Theorem of Calculus.

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Chapter 4 Solutions