Question

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).

Answer #1

a) Find the domain and range of the following function:
f(x,y)=sin(ln(x+y))
b) sketch the domain.
c) on seperate graph, sketch three level curves

Given ?(?,?) = sqrt(x + y)
a). What’s the domain and range of f(x, y)?
b). Sketch any 3 level curves in the domain of the function (on
the same graph). Label any points where the level curves cross an
axis AND label the value of f(x, y) on each curve.
c. Please do the same for g(x,y)= -y/x^2

6. Consider the function f defined by f (x, y) = ln(x
− y). (a) Determine the natural domain of f. (b) Sketch the level
curves of f for the values k = −2, 0, 2. (c) Find the gradient of f
at the point (2,1), that is ∇f(2,1). (d) In which unit vector
direction, at the point (2,1), is the directional derivative of f
the smallest and what is the directional derivative in that
direction?

Given?(?,?)= 9− ?^2
a). State the function’s domain and range.
b). Sketch the surface in 3-D. Be sure to clearly label your
axes and label any points on the surface that cross an axis.
c). On a separate graph from part (b), sketch the following
level curves in the domain of the function: f(x, y) = 0, f(x, y) =
5, and f(x, y) = 9. Label the value of f(x, y) on each level
curve.

Consider the function f(x,y)= (x+2*y)*e^(x-2y) for all real
values (x,y).
Determine the linearization to f at the point (2,1)
Use the linearization to approximate f(2.1,1.1)

Find the inverse function of f(x)= 1+2cos(x) and then find the
domain and the range of the function of both f and f^-1??
Find the inverse function of f(x)=sqrt(3-e^2x) and then find the
domain and the range of the function of both f and f^-1??

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).

The domain of the function g(x) is -1<x<6 and
the range is -5<y<10.
Find the domain and range of the following given functions.
a). the domain of y=g(x-4) is?
b.) the range of y=g(x)+2 is?

Let f(x, y) = x^2 ln(x^3 + y).
(a) Find the gradient of f.
(b) Find the direction in which the function decreases most
rapidly at the point P(2, 1). (Give the direction as a unit
vector.)
(c) Find the directions of zero change of f at the point P(2,
1). (Give both directions as a unit vector.)

Let f(x, y) = sqrt( x^2 − y − 4) ln(xy).
• Plot the domain of f(x, y) on the xy-plane.
• Find the equation for the tangent plane to the surface at the
point (4, 1/4 , 0).
Give full explanation of your work

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 25 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago