Question

Use both the local linear and local quadratic approximation to estimate f(0.1, −0.1) where f(x, y) = cos(x + y)e x−y .

Answer #1

A) Use the Linear Approximation to estimate Δf
= f(4.9) − f(5) for
f(x) = x −
6x2.
Δf ≈
B)Estimate the actual change.
Δf =
C)Compute the error in the Linear Approximation
D)Compute the percentage error in the Linear Approximation.
(Round your answer to five decimal places.)

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

-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)

Estimate ΔfΔf using the Linear Approximation and use a
calculator to compute both the error and the percentage
error.
f(x)=sqrt(19+x) .a=6.Δx=−0.5
With these calculations, we have determined that the square root
is approximately
The error in Linear Approximation is:
The error in percentage terms is:

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 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)=_________

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...

Consider the function f(x)= squareroot of (3x)
1) find the linear approximation to the function f at a=4
2) use the linear approximation from part 1 to estimate
squareroot of (12.6)

Use Euler's method with step size 0.1 to estimate y(0.5), where
y(x) is the solution of the initial-value problem
y'=3x+y^2, y(0)=−1
y(0.5)=

Consider the function f(x,y) = xe^((x^2)-(y^2))
(a) Find f(1,−1), fx(1,−1), fy(1,−1). Use these values to find a
linear approximation for f (1.1, −0.9).
(b) Find fxx(1, −1), fxy(1, −1), fyy(1, −1). Use these values to
find a quadratic approximation for f(1.1,−0.9).

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