Question

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) =

Answer #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)=_________

Find a Linearization L(x,y) of the function at each point.
f(x,y)=x^2+y^2+1
a) (4,2)
b) (3,2)

Find the linearization of the function f (x y) =
arctan (y / x) at point (1,1) and the tangent plane at that
point.

Find the linearization of the function f(x,y) = √xy at the point
P(1,1) to approximate f(4/5, 11/10).

Let f(x) = 3sqrtx.
Find the linear linearization of f(x) at x=216
L(x)=
Use the above result to approximate 3sqrt218. Write
your answer as a fraction.
3sqrt218=

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)

-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)

For f(x,y)=ln(x^2−y+3). -> Find the domain
and the range of the function z=f(x,y).
-> Sketch the domain, then
separately sketch three distinct level curves.
-> Find the linearization of
f(x,y) at the point
(x,y)=(4,18).
-> Use this linearization to determine the
approximate value of the function at the point (3.7,17.7).

F(x,y) = (x2+y3+xy,
x3-y2)
a) Find the linearization of F at the point (-1,-1)
b) Explain that F has an inverse function G defined in an area
of (1, −2) such that
that G (1, −2) = (−1, −1), and write down the linearization to G in
(1, −2)

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).

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