Duplicate of Multivariable Calculus Partial Derivatives Test Review

Question 1

The directional derivative of z = (x^2)(e^-y) at the point (-1,0) in the direction of (4,-3) is

Accepted Answer

-1

Question 2

A gradient at a point will behave how relative to a level curve?

Accepted Answer

perpendicular

Question 3

See question...

Accepted Answer

16 and 8

Question 4

The "D" in the multivariable second derivative test is:

Accepted Answer

fxxfyy - (fxy)2

Question 5

Given f(x,y) below and x = sin(2t) and y = cos t, find dz/dt when t = 0.

Accepted Answer

6

Question 6

The "Lagrange multiplier" method is

Accepted Answer

a way to solve constraint problems

Question 7

A PringleTM is an example of a(n) _____

Accepted Answer

all of the above

Question 8

Find the equation of the tangent plane to f(x,y) = (e^x)(Cos y) at the point (0,0,1).

Accepted Answer

z = x + 1

Question 9

Which equation below gives the graph of this quadric surface?

Accepted Answer

4x^2 - y^2 - z + 8x + 8z + 24 = 0

Question 10

A gradient is a(n) _____

Accepted Answer

vector

Question 11

I am ready for the test on Friday! True or False.

Accepted Answer

True

Question 12

Given f(x, y, z) = x30y26z, what is fxyzyzzyyxx?

Accepted Answer

0

Question 13

∇f(x, y), where f(x, y) = 10x5y is

Accepted Answer

<50x4y, 10x5>

Question 14

Evaluate the limit:

Accepted Answer

Does not exist

Question 15

Clairaut's Theorem states that _____

Accepted Answer

fxy = fyx

Question 16

Is fxy at P positive or negative?

Accepted Answer

positive

Question 17

If fxxfyy - (fxy)2 < 0, this means . . .

Accepted Answer

saddle point

Question 18

A gradient points in what direction?

Accepted Answer

maximum rate of change

Questions 18