Consider the following approximations for a function f(x, y) centered at (0, 0). Linear approximation: P;(x, y) = F(0, 0) + ,(0, 0)x + f,(0, 0)y Quadratic approximation: Pa(x, V) = FR0, 0) + f„(0, 0)x + F,(0, 0)y +f(0, 0)x² + f„(0, 0)xy + f(0, 0)y² [Note that the linear approximation is the tangent plane to the surface at (0, o, f(0, 0)).] (a) Find the linear approximation of f(x, y) = e(x - y) centered at (0, 0). P1(0, 0) = | (b) Find the quadratic approximation of f(x, y) = e(x = y) centered at (0, 0). P2(0, 0) = (c) If x = 0 in the quadratic approximation, you obtain the second-degree Taylor polynomial for what function? Answer the same question for y = 0.
Consider the following approximations for a function f(x, y) centered at (0, 0). Linear approximation: P;(x, y) = F(0, 0) + ,(0, 0)x + f,(0, 0)y Quadratic approximation: Pa(x, V) = FR0, 0) + f„(0, 0)x + F,(0, 0)y +f(0, 0)x² + f„(0, 0)xy + f(0, 0)y² [Note that the linear approximation is the tangent plane to the surface at (0, o, f(0, 0)).] (a) Find the linear approximation of f(x, y) = e(x - y) centered at (0, 0). P1(0, 0) = | (b) Find the quadratic approximation of f(x, y) = e(x = y) centered at (0, 0). P2(0, 0) = (c) If x = 0 in the quadratic approximation, you obtain the second-degree Taylor polynomial for what function? Answer the same question for y = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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![Consider the following approximations for a function f(x, y) centered at (0, 0).
Linear approximation:
P,(x, y) = f(0, 0) + f,(0, 0)x + f,(0, 0)y
Quadratic approximation:
P2(x, v) = F(0, 0) + f,(0, 0)x + f,(0, 0)y +ica(0, 0)x² + f„(0, 0)xy + fy,(0, 0)y²
[Note that the linear approximation is the tangent plane to the surface at (0, 0, f(0, 0)).]
(a) Find the linear approximation of f(x, y) = ex -) centered at (o, 0).
P;(0, 0) =
(b) Find the quadratic approximation of f(x, y) = ex - y) centered at (0, 0).
P2(0, 0) =
(c) If x = 0 in the quadratic approximation, you obtain the second-degree Taylor polynomial for what function?
O eY
O ex
O e-Y
Answer the same question for y = 0.
O e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff17d012-70ad-4782-80ac-5077bdfc24e1%2F91e04520-788e-46be-9fd6-adbf2e834e70%2Fuepaic5_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following approximations for a function f(x, y) centered at (0, 0).
Linear approximation:
P,(x, y) = f(0, 0) + f,(0, 0)x + f,(0, 0)y
Quadratic approximation:
P2(x, v) = F(0, 0) + f,(0, 0)x + f,(0, 0)y +ica(0, 0)x² + f„(0, 0)xy + fy,(0, 0)y²
[Note that the linear approximation is the tangent plane to the surface at (0, 0, f(0, 0)).]
(a) Find the linear approximation of f(x, y) = ex -) centered at (o, 0).
P;(0, 0) =
(b) Find the quadratic approximation of f(x, y) = ex - y) centered at (0, 0).
P2(0, 0) =
(c) If x = 0 in the quadratic approximation, you obtain the second-degree Taylor polynomial for what function?
O eY
O ex
O e-Y
Answer the same question for y = 0.
O e
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