Question

Find the linear approximation L(x) to y = xsinx for values of x near a = π

Answer #1

Find the linearization of the function
f(x,y)=40−4x2−2y2−−−−−−−−−−−−√f(x,y)=40−4x2−2y2 at the point (1,
4).
L(x,y)=L(x,y)=
Use the linear approximation to estimate the value of
f(0.9,4.1)f(0.9,4.1) =

Find the quadratic approximation (Taylor Polynomial) for f(x,y)
= 2xe^(2y) near (2,0).

Find the linearization of the function
f(x,y)=√(22−1x2−3y2 )at the point (-1,
2).
L(x,y)=_______
Use the linear approximation to estimate the value of
f(−1.1,2.1)=_________

Find the local linear approximation of f(x,y) = x + tan(xy - 6)
at the point (3,2)

Complete steps (i)-(vii) below in order to estimate the
following values using linear approximation: (a) cos(31π/ 180) (i)
Identify the function, f(x). (ii) Find the nearby value where the
function can be easily calculated, x = a. (iii) Find ∆x = dx. (iv)
Find the linear approximation, L(x). (v) Compute the approximate
value of the expression using the linear approximation. (vi)
Compare the approximated value to the value given by your
calculator. (vii) Compare dy and ∆y using the value...

find general solution y’’ + y’ + y = xsinx

-find the differential and linear approximation of f(x,y) =
sqrt(x^2+y^3) at the point (1,2)
-use tge differential to estimate f(1.04,1.98)

Assume that 1+2x is the linear approximation for sqrt(1+4x) near
x = 0. Use it to approximate sqrt(0.76) and then compute the
absolute error and relative error of this approximation.

3.Find the four second partial derivatives of z =
2xey - 3ye-x
4.Find the linear approximation to f(x, y) = (x + y) / (x - y)
at the point (3, 2). Then use the approximation to estimate f(2.95,
2.05).

Find the linear approximation of the function f(x, y, z) = x2 +
y2 + z2 at (6, 2, 9) and use it to approximate the number 6.012 +
1.972 + 8.982 . (Round your answer to five decimal places.) f(6.01,
1.97, 8.98) ≈

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