Find the quadratic approximation of the function about a point (0,0) using second order and third...

Find the quadratic approximation of the function about a point (0,0) using second order and third order of Taylor's Series Expansion for f(x,y)=x^2 + e^siny and then f(x,y)= sin(x+y)+ xe^-y

Expert Solution

Colby Messinger answered 1 year ago

Find the best quadratic approximation to f(x,y) = e4ycos(-3x) about the origin (0,0) and estimate the...

Find the best quadratic approximation to f(x,y) = e4ycos(-3x) about the origin (0,0) and estimate the value when this approximation is used to calculate f(0.1,0.1).Do not do the error approximation. Also, find the extreme values of the function f(x,y,z) = 8y2-4xz +16z - 35 on the surface 2x2+4y2+4z2 = 64

Find the best quadratic approximation to f(x,y) = e5ycos(-4x) about the origin (0,0) and estimate the...

Find the best quadratic approximation to f(x,y) = e5ycos(-4x) about the origin (0,0) and estimate the value when this approximation is used to calculate f(0.1,0.1).Do not do the error approximation. Also, find the extreme values of the function f(x,y,z) = 8y2-4xz +16z - 35 on the surface 2x2+4y2+4z2 = 32 Thank you for your help

Calculate the second-order Taylor approximation to f(x, y) = 3 cos(x) sin(y) at the point (pi,...

Calculate the second-order Taylor approximation to f(x, y) = 3 cos(x) sin(y) at the point (pi, pi/2)

Describe direct, first, second, and third order control system.

a. Find the nth-order Taylor polynomials of the given function centered at the given point a,...

a. Find the nth-order Taylor polynomials of the given function centered at the given point a, for n = 0, 1, and 2. b. Graph the Taylor polynomials and the function. f(x) = cos x, a = 2pi / 3

Sometimes calculating a business profit requires using a quadratic function. Think about how the problems presented...

Sometimes calculating a business profit requires using a quadratic function. Think about how the problems presented below might involve a quadratic and how it could involve a business calculation. People frequently need to calculate the area of rooms, boxes or plots of land. An example might involve building a rectangular lawn or room where one side must be twice or three times the length of the other side. For example, if you have to paint the room or lay down...

Problem 3: Find a second solution by reduction of order - nonhomogeneous The given function y1(x)...

Problem 3: Find a second solution by reduction of order - nonhomogeneous The given function y1(x) is a solution of the associated homogeneous equation. Use the reduction of order method to ﬁnd a solution y(x) = u(x)y1(x) of the nonhomogeneous equation. 1. x^2y'' + xy'−4y = x^3, y1 = x^2 2. 2x^2*y'' + 3xy'−y = 1/x , y1 = x^(1/2)

What quantity must be small to ensure the validity of the Fresnel approximation (Use the second-order...

What quantity must be small to ensure the validity of the Fresnel approximation (Use the second-order term of the Taylor series expansion)?

Find an approximation of the area of the region R under the graph of the function...

Find an approximation of the area of the region R under the graph of the function f on the interval [1, 3]. Use n = 4 subintervals. Choose the representative points to be the right endpoints of the subintervals. f(x)=6/x Find the area of the region under the graph of the function f on the interval [3, 7]. Find the area of the region under the graph of the function f on the interval [-27, -1]. Find the area of...

Find maximum, minimum and saddle point by using the second derivative test: Show all the work...

Find maximum, minimum and saddle point by using the second derivative test: Show all the work f(x, y) =8xy-x^4-y^4

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