Question

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).

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).

-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)

Consider the function f(x,y)=y+sin(x/y)
a) Find the equation of the tangent plane to the graph offat the
point(1,3)
b) Find the linearization of the function f at the point(1;3)and
use it to approximate f(0:9;3:1).
c) Explain why f is differentiable at the point(1;3)
d)Find the differential of f
e) If (x,y) changes from (1,3) to (0.9,3.1), compare the values
of ‘change in f’ and df

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).

For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find the unit vectors U+ and
U- , that give the direction of steepest ascent and the steepest
descent respectively.

Use variation of parameters to solve the following differential
equations
y''+4y'+4y=e^(t)tan^-1(t)

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)

Find the general solution of the differential equation
10y' + 4y/x = 1/y^4

f(x,y)=-e^(3x^2+6y^2)+e^(5y^2+1) identify the shape of
the level curve which contains (-sqrt(3)/3,0)
take as the parallelogram bounded by
x-y=0, x-y=3, x+2y=0, x+2y=2
(9x+3y)dxdy

Solve the differential equation:
y' = sqrt((y-x)/x) + 1
y(1) = 10

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