Question 1

Find the indicated partial derivative. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indicated partial derivative. 
A) 
B)...

Question 2

Find the limit 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the limit 
A) 
B) 
C) 
D)...

Question 3

Use implicit differentiation to find  
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use implicit differentiation to find  
A)...

Question 4

Find the limit 
A) 34
B) 16
C) 80
D) 260

Accepted Answer

There is no variable or function in the limit expression, so we can simply evaluate it. 11eaae29_f463_1de3_87fe_31f82091107f_TB2067_11 is a constant and does not change with x. Therefore, as x approaches any value, the limit will still be 11eaae29_f463_1de3_87fe_31f82091107f_TB2067_11. Evaluating this constant gives us approximately 16.

Question 5

How many nth-order partial derivatives does a function of two variables have?
A) 
B) 
C) 
D) 
E)

Accepted Answer

For a function of two variables, the nth order partial derivative can be found by taking the partial derivative of the (n-1)th order partial derivative with respect to one of the variables. Therefore, the total number of nth order partial derivatives is the number of ways to distribute n derivatives between the two variables without over-counting. This is given by the binomial coefficient (n+2 choose 2), which simplifies to (n+2)(n+1)/2. For n = 0, 1, 2, ..., the values of this expression are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, ... The 10th term in this sequence is 66, so the correct answer is D.

Question 6

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 7

Find all the second partial derivatives.

Accepted Answer

The answer of Find all the second partial derivatives. ...

Question 8

Use implicit differentiation to find  
A) 
B) 
C) 
D)

Accepted Answer

Let y = 11e^x, then y' = 11e^x
Differentiating both sides with respect to x:
y'' = (11e^x)' = 11e^x
Substituting back y = 11e^aae29_f45f_c354_87fe_e58298ba1b8e_TB2067_11:
y'' = 11e^(11eaae29_f45f_c354_87fe_e58298ba1b8e_TB2067_11)
Therefore, the answer is 11eaae29_f45f_ea67_87fe_6f5432fdea7c_TB2067_11.

Question 9

Find  for  .

Accepted Answer

The answer of Find  for  ....

Question 10

Determine the largest set on which the function is continuous. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Determine the largest set on which the...

Question 11

Find the indicated partial derivative. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the indicated partial derivative. 
A) 
B)...

Question 12

The ellipsoid  intersects the plane  in an ellipse.Find parametric equations for the tangent line to this ellipse at the point (1,2,2).
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The ellipsoid  intersects the plane ...

Question 13

Find the first partial derivatives of the function.

Accepted Answer

The answer of Find the first partial derivatives of the...

Question 14

Use partial derivatives to find the implicit derivative

Accepted Answer

The answer of Use partial derivatives to find the implicit...

Question 15

Find  .

Accepted Answer

The answer of Find  . ...

Question 16

Find the limit 
A) 
B) 
C) 
D)

Accepted Answer

The limit is a value that a function approaches as the independent variable approaches a certain value. From the options given, only option C has a different fourth set of digits (ba2c instead of ba2b or e13d) which suggests that it represents a different limit. Therefore, C is the best choice.

Question 17

Evaluate the limit. 
A) 1
B) 0
C) 
D) 2
E) the limit does not exist

Accepted Answer

The answer of Evaluate the limit. 
A) 1
B) 0
C) 
D)...

Question 18

Evaluate the limit. 
A) 
B) 
C) 0
D) 
E)

Accepted Answer

The answer of Evaluate the limit. 
A) 
B) 
C) 0
D)...

Question 19

Find the first partial derivatives of the function

Accepted Answer

The answer of Find the first partial derivatives of the...

Question 20

Find the limit 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the limit 
A) 
B) 
C) 
D)...

Quiz 11: Partial Derivatives

Find the indicated partial derivative.

Find the limit

Use implicit differentiation to find

Find the limit

How many nth-order partial derivatives does a function of two variables have?

Find the differential of the function.

Find all the second partial derivatives.

Use implicit differentiation to find

Find for .

Determine the largest set on which the function is continuous.

Find the indicated partial derivative.

The ellipsoid intersects the plane in an ellipse.Find parametric equations for the tangent line to this ellipse at the point (1,2,2) .

Find the first partial derivatives of the function.

Use partial derivatives to find the implicit derivative

Find .

Find the limit

Evaluate the limit.

Evaluate the limit.

Find the first partial derivatives of the function

Find the limit