Explanation Formula used: Taylor’s formula for f ( x , y ) at the origin for quadratic and cubic approximation. f ( x , y ) = f ( 0 , 0 ) + x f x ( 0 , 0 ) + y f y ( 0 , 0 ) + 1 2 ! ( x 2 f x x ( 0 , 0 ) + 2 x y f x y ( 0 , 0 ) + y 2 f y y ( 0 , 0 ) ) + 1 3 ! ( x 3 f x x x ( 0 , 0 ) + 3 x 2 y f x x y ( 0 , 0 ) + 3 x y 2 f x y y ( 0 , 0 ) + y 3 f y y y ( 0 , 0 ) ) Calculation: Consider the given function f ( x , y ) = e x cos y . Here, the values that are required for substituting in the Taylor’s formula is evaluated as follows. f ( 0 , 0 ) = 1 , f x = e x cos y , f y = − e y sin y , f x x = e x cos y , f x y = − e x sin y , f y y = − e x cos y , f x x x = e x cos y , f x x y = − e x sin y , f x y y = − e x cos y , f y y y = e x sin y In the above calculation f x and f y are obtained by partially differentiating the given function with respect to x and y . Now, the substitute the values in the above mentioned Taylor’s formula to obtain the quadratic approximation

Thomas' Calculus: Early Transcendentals (14th Edition)

14th Edition

ISBN: 9780134439020

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 14.9, Problem 2E

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To evaluate: The quadratic and cubic approximations of the function f(x,y)=excosy near the origin using the Taylor’s formula for f(x,y) at the origin.

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Chapter 14.9, Problem 1E

Chapter 14.9, Problem 3E

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Chapter 14 Solutions

Thomas' Calculus: Early Transcendentals (14th Edition)

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The quadratic and cubic approximations of the function f ( x , y ) = e x cos y near the origin using the Taylor’s formula for f ( x , y ) at the origin.

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To evaluate: The quadratic and cubic approximations of the function f(x,y)=excosy near the origin using the Taylor’s formula for f(x,y) at the origin.

Want to see the full answer?

Chapter 14 Solutions