Explanation Given: f ( x ) = x , n = 2 , a = 4 Concept Used: The Taylor polynomial of degree n of function f centered at a is T n ( x ) = f ( a ) + f ′ ( a ) ( x − a ) + f ″ ( a ) 2 ! ( x − a ) 2 + .... + f ″ ( a ) n ! ( x − a ) n Calculation: To find the Taylor polynomial of degree n = 2 of function f ( x ) = x , centered at the number a = 4 , first find f ( 4 ) , f ′ ( 4 ) , and f ″ ( 4 ) as f ( 4 ) = 4 = 2 , f ′ ( x ) = d d x ( x ) = 1 2 x ⇒ f ′ ( 4 ) = 1 2 4 = 1 4 , f ″ ( x ) = d d x f ′ = d d x ( 1 2 x ) = 1 2 d d x ( x − 1 / 2 ) = 1 2 ( − 1 / 2 ) x − 1 / 2 − 1 = − 1 4 x 3 / 2

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.8, Problem 38E

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To find the Taylor polynomial of degree n=2of function f(x)=x , centered at the number a=4

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Chapter 3.8, Problem 37E

Chapter 3.8, Problem 39E

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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

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

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

Chapter 3 Solutions

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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To find the Taylor polynomial of degree n = 2 of function f ( x ) = x , centered at the number a = 4

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