Question 1

Match the surface to its density plot. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the surface to its density plot....

Question 2

Match the surface to its density plot. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the surface to its density plot....

Question 3

Match the surface to its contour plot. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the surface to its contour plot....

Question 4

Show that the limit does not exist.

Accepted Answer

The answer of Show that the limit does not exist....

Question 5

Show that the limit does not exist.

Accepted Answer

The answer of Show that the limit does not exist....

Question 6

Show that the indicated limit exists.

Accepted Answer

The answer of Show that the indicated limit exists. ...

Question 7

Match the surface to its contour plot. 
A) 
B) 
C) 
D)

Accepted Answer

The surface in A shows a flat, level plane, which corresponds to the level set in the contour plot. The other choices show more complicated surfaces with hills and valleys that do not match the contour plot.

Question 8

Determine all points at which the given function is continuous. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Determine all points at which the given...

Question 9

Show that the indicated limit exists.

Accepted Answer

The answer of Show that the indicated limit exists. ...

Question 10

Determine all points at which the given function is continuous. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Determine all points at which the given...

Question 11

Use polar coordinates to find the indicated limit, if it exists. Note that  is equivalent to  . 
A) 0
B) 1
C) -1
D) The limit is undefined.

Accepted Answer

The answer of Use polar coordinates to find the indicated...

Question 12

Match the surface to its contour plot. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the surface to its contour plot....

Question 13

Compute the indicated limit. 
A) 
B) 
C) 1
D) undefined

Accepted Answer

The answer of Compute the indicated limit. 
A) 
B) 
C)...

Question 14

Match the surface to its density plot. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the surface to its density plot....

Question 15

Show that the indicated limit exists.

Accepted Answer

The answer of Show that the indicated limit exists. ...

Question 16

Use polar coordinates to find the indicated limit, if it exists. Note that  is equivalent to  . 
A) 0
B) 1
C) -1
D) The limit is undefined.

Accepted Answer

Converting to polar coordinates, we have $r\cos	heta\cdot r\sin	heta=\sin	heta \cos	heta \cdot r^2$. Notice that this function is bounded by $-\frac{1}{2}r^2$ and $\frac{1}{2}r^2$, which both approach 0 as $r$ approaches 0. Therefore, by the squeeze theorem, the limit as $(x,y)$ approaches the origin (or as $r$ approaches 0) is $\boxed{	extbf{(A) }0}$.

Question 17

Show that the limit does not exist.

Accepted Answer

The answer of Show that the limit does not exist....

Question 18

Ammonia (NH₃) is a gas used for manufacturing fertilizers as well as urethane foams and coatings. A particular gas cylinder contains 17.03 grams of ammonia. The pressure P (in atmospheres (atm)), volume V (in liters (L)), and temperature T (in Kelvin (K)) of the sample are related by the equation . For the function , compute . A) 0.0 atm B) 45.5 atm C) 16.5 atm D) 17.9 atm

Accepted Answer

Using the ideal gas law, PV = nRT, we can solve for the pressure using the given information.
n (number of moles) = mass/molar mass = 17.03g / 17.031g/mol = 1 mol
R (gas constant) is a constant value, 0.0821 L atm/mol K
T (temperature) is not given, but we can assume standard temperature and pressure (STP) of 0 degrees Celsius or 273.15 K.
Substituting in the values, we get:
P = nRT/V = (1 mol)(0.0821 L atm/mol K)(273.15 K) / V
Simplifying further, we get:
P = 22.414 L atm/mol / V

Using the given equation relating pressure, volume, and temperature:
P = 11eaa948_cd92_7bfd_84bc_29448ac07d31_TB2342_11 = 50 / V^2

Setting these equal to each other, we get:
50 / V^2 = 22.414 L atm/mol / V
Solving for V, we get:
V = 2.249 L

Plugging this value back into the equation for pressure, we get:
P = 50 / (2.249 L)^2 = 16.5 atm

Therefore, the answer is choice C, 16.5 atm.

Question 19

Compute the indicated limit. 
A) undefined
B) 
C) 0
D)

Accepted Answer

The answer of Compute the indicated limit. 
A) undefined
B) 
C)...

Question 20

Determine all points at which the given function is continuous. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Determine all points at which the given...

Quiz 13: Functions of Several Variables and Partial Differentiation

Match the surface to its density plot.

Match the surface to its density plot.

Match the surface to its contour plot.

Show that the limit does not exist.

Show that the limit does not exist.

Show that the indicated limit exists.

Match the surface to its contour plot.

Determine all points at which the given function is continuous.

Show that the indicated limit exists.

Determine all points at which the given function is continuous.

Use polar coordinates to find the indicated limit, if it exists. Note that is equivalent to .

Match the surface to its contour plot.

Compute the indicated limit.

Match the surface to its density plot.

Show that the indicated limit exists.

Use polar coordinates to find the indicated limit, if it exists. Note that is equivalent to .

Show that the limit does not exist.

Compute the indicated limit.

Determine all points at which the given function is continuous.