Question 1

Use the four step process to find f'(x) for the function .

Accepted Answer

C

Question 2

Accepted Answer

C

Question 3

Accepted Answer

C

Question 4

f(x) =

Accepted Answer

The answer of f(x) = 
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Question 5

Is f continuous at x = 0?

Accepted Answer

To determine if f is continuous at x=0, we need to check if the limit of f(x) as x approaches 0 from both the left and the right sides is equal to f(0). Let's evaluate both limits:

Limit as x approaches 0 from the left: 
lim(x->0-) f(x) = lim(x->0-) (-2x) = 0

Limit as x approaches 0 from the right: 
lim(x->0+) f(x) = lim(x->0+) (3x) = 0

Since lim(x->0-) f(x) is not equal to lim(x->0+) f(x), f is not continuous at x=0. The correct choice is B.

Question 6

Accepted Answer

The answer of 
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Question 7

Use the graph of f given below to find f(-10).

Accepted Answer

The answer of Use the graph of f given below...

Question 8

Accepted Answer

The answer of 
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Question 9

Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y =

Accepted Answer

The answer of Find the average rate of change of...

Question 10

Is f continuous at x = 0?

Accepted Answer

To determine if f is continuous at x=0 we must evaluate the limit of f(x) as x approaches 0 from both the left and right sides, and see if those limits are equal to f(0).

As x approaches 0 from the left side, we have:

f(x) = -x+1 if -1 < x < 0
         = 0 if x = 0

So the limit of f(x) as x approaches 0 from the left is:

lim f(x) = lim(-x+1) = 1
x→0-

As x approaches 0 from the right side, we have:

f(x) = x+1 if 0 < x < 1
         = 0 if x = 0

So the limit of f(x) as x approaches 0 from the right is:

lim f(x) = lim(x+1) = 1
x→0+

Since both the left and right limits equal 1, and f(0) = 0, then the limit of f(x) as x approaches 0 exists and is equal to f(0). Therefore, f is continuous at x = 0. The best choice is B.

Question 11

Accepted Answer

The answer of   ...

Question 12

Find: lim x·- 4

Accepted Answer

When multiplying any number with -4, the result will always be negative. As x approaches 0 from either positive or negative side, the result will approach -0 or just 0. Therefore, the limit of x times -4 as x approaches 0 is -0 or just 0 which is equivalent to -8 when multiplied with a negative sign. So, the correct choice is D.

Question 13

f(x) =

Accepted Answer

The answer of f(x) = 
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Question 14

Is f continuous at x = -0.5?

Accepted Answer

In order for f to be continuous at x = -0.5, the limit of f(x) as x approaches -0.5 must exist and be equal to f(-0.5).

Taking the limit as x approaches -0.5 from the left, we get:

lim x → -0.5- f(x) = lim x → -0.5- (x + 1) = -0.5 + 1 = 0.5

Taking the limit as x approaches -0.5 from the right, we get:

lim x → -0.5+ f(x) = lim x → -0.5+ (x² + 2x) = (-0.5)² + 2(-0.5) = -0.25

Since the limit from the left is not equal to the limit from the right, the limit as x approaches -0.5 does not exist. Therefore, f is not continuous at x = -0.5.

Therefore, the answer is B) No.

Question 15

Determine the limit.

Accepted Answer

The answer of Determine the limit. 
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Question 16

The cost of renting a snowblower is $20 for the first hour (or any fraction thereof)and $5 for each additional hour (or fraction thereof)up to a maximum rental time of 5 hours.Write a piecewise definition of the cost C(x)of renting a snowblower for x hours.Is C(x)continuous at x = 2.5?

Accepted Answer

The answer of The cost of renting a snowblower is...

Question 17

Accepted Answer

The answer of ...

Question 18

C(x).

Accepted Answer

The answer of   C(x).
...

Question 19

Accepted Answer

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Question 20

Accepted Answer

The answer of  ...

Quiz 11: Mathematical Functions and Limits

Use the four step process to find f'(x) for the function .

f(x) =

Is f continuous at x = 0?

Use the graph of f given below to find f(-10) .

Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y =

Is f continuous at x = 0?

Find: lim x·- 4

f(x) =

Is f continuous at x = -0.5?

Determine the limit.

C(x) .