Question

-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)

Answer #1

Find the differential of f(x,y)=sqrt(x2+y3) at the point
(2,3).
Then use the differential to estimate f(2.04,2.96).

1.
The linearization of f(x)=(e^x^2) at x=1 is?
2. The linear approximation of f(x)=sqrt(x+3) is?
3. compute the average value of f(x)=(x^3)+(3x^2) over
interval [1,2] is?

Find the linear approximation of the function f(x, y, z) = sqrt
x2 + y2 + z2 at (3, 6, 6) and use it to approximate the number
sqrt3.01^2 + 5.97^2 + 5.98^2 . (Round your answer to five decimal
places.) f(3.01, 5.97, 5.98)

Let f(x,y) = sqrt(22−2x^2−y^2). Find the linearization of the
function f at (1,2) and use it to approximate f(1.1,2.1).

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)=_________

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).

1. Find the differential of f(x,y)=\sqrt{x + e^{4y}}f(x,y)=
x+e^4y and use it to find the approximate change in the function
f(x,y)f(x,y) as (x,y)(x,y) changes from (3,0)(3,0) to
(2.6,0.1)(2.6,0.1).

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

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) =

1) which of the following is a linear approximation of the
function f(x)= sqrt[ 4 ] { x } at a=16.
2) determine the number of inflection points on the graph of
the function f(x)=x^5-x^4.
3) determine the sum of the critical numbers for the function
f(x)=x^3+3x^2-9x.

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