Solve the problem. What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a?

Group of answer choices

The limit ofasfrom the left exists, the limit ofasfrom the right exists, and these two limits are the same.

Either the limit ofasfrom the left exists or the limit ofasfrom the right exists

f(a) exists, the limit ofasfrom the left exists, and the limit ofasfrom the right exists.

The limit ofasfrom the left exists, the limit ofasfrom the right exists, and at least one of these limits is the same as f(a).

Flag question: Question 2Question 21pts

Decide whether the limit exists. If it exists, find its value. f(x) andf(x)

Group of answer choices

-3; -1

3; -1

3; 1

-1; 3

Flag question: Question 3Question 31pts

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.

Group of answer choices

6

0

Flag question: Question 4Question 41pts

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.

Group of answer choices

10

Does not exist

20

1

Flag question: Question 5Question 51pts

Find the limit. 5 x²+ 12x - x

Group of answer choices

12

6

0

Flag question: Question 6Question 61pts

Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.

Group of answer choices

0

-

Flag question: Question 7Question 71pts

Find the limit, if it exists.

Group of answer choices

0

-

Flag question: Question 8Question 81pts

Find all points where the function is discontinuous.

Group of answer choices

x = -2, x = 1

x = 1

x = -2

None

Flag question: Question 9Question 91pts

The graph of y = f(x) is shown. Use the graph to answer the question. Is f continuous at x = -1?

Group of answer choices

No

Yes

Flag question: Question 10Question 101pts

Answer the question. Is the function given by 1 " data-api-endpoint="https://mdc.instructure.com/api/v1/courses/22570/files/12683205" data-api-returntype="File" data-id="12683205" style="max-width: 100%; height: auto; vertical-align: -4px; border: 0px;"> continuous at x = 1? Why or why not?

Group of answer choices

Yes,f(x) = f(1)

No,f(x) does not exist

Flag question: Question 11Question 111pts

Use the definition f'(x) =to find the derivative of the following function with respect to x. f(x) = -21x - 3

Group of answer choices

-21

21

18

21x

Flag question: Question 12Question 121pts

The figure shows the graph of a function. At the given value of x, does the function appear to be differentiable, continuous but not differentiable, or neither continuous nor differentiable? x = -1

Group of answer choices

Continuous but not differentiable

Differentiable

Neither continuous nor differentiable

Flag question: Question 13Question 131pts

List the x-values in the graph at which the function is not differentiable.

Group of answer choices

x = 2

x = 1

x = 0

x = -1

Flag question: Question 14Question 141pts

Use the differentiation feature on a graphing calculator to find the indicated derivative. f(x) = 0.21x³- 1.62x²+ 4.50x + 8.7; f'(-3)

Group of answer choices

28.590

-18.990

15.030

19.890

Flag question: Question 15Question 151pts

Find dy/dx. y =

Group of answer choices

+

-

-

x^3/2+ 7

Flag question: Question 16Question 161pts

Differentiate. f(x) = (4x - 5)(3x³- x²+ 1)(Using Product Rule)

Group of answer choices

12x³+ 19x²- 57x + 4

36x³+ 57x²- 19x + 4

48x³- 57x²+ 10x + 4

48x³- 19x²+ 57x + 4

Flag question: Question 17Question 171pts

Differentiate. g(x) =(Using Quotient Rule)

Group of answer choices

Flag question: Question 18Question 181pts

Find the slope of the line tangent to the graph of the function at the given value of x (using the derivative of the given function). y = x⁴+ 8x³+ 2x + 2; x = 1

Group of answer choices

30

27

29

32

Flag question: Question 19Question 191pts

Provide an appropriate response. Find the equation of the tangent line at x = - 6 for f(x) =. Write the answer in the form y = mx + b.

Group of answer choices

y = 54x + 216

y = 216x + 54

y = 18x + 216

y = 216x + 18

Flag question: Question 20Question 201pts

Find the indicated derivative of the function. of y = 2x⁶- 2x⁴+ 4x²

Group of answer choices

480x²- 24

720x²- 48x

720x²- 48

480x²- 24x

Flag question: Question 21Question 211pts

Find an expression for dy/dx. y =and u = 6x - 7

Group of answer choices

-

-

-

Flag question: Question 22Question 221pts

Find an expression for dy/dx. y = u^-7/4and u = x²- 9x - 5

Group of answer choices

Flag question: Question 23Question 231pts

Differentiate. y = (3x²+ 3)⁵(Using Chain Rule)

Group of answer choices

30x(3x²+ 3)⁴

5(3x²+ 3)⁴

30(3x²+ 3)⁴

(30x + 3)(3x²+ 3)⁴

Flag question: Question 24Question 241pts

Differentiate. y =(Using Chain Rule)

Group of answer choices

Flag question: Question 25Question 251pts

Find the equation of the line tangent to the graph of the function at the indicated point. y =at the point (2,)

Group of answer choices

y =(x - 2) +

y = 2(x - 2) -

y = -(x - 2) +

y =(x - 2) +

Flag question: Question 26Question 261pts

Solve the problem. The total cost, in dollars, to produce x DVD players isFind the marginal cost when

Group of answer choices

$754

$874

$2120

$2000

Flag question: Question 27Question 271pts

Solve the problem. The profit, in dollars, from the sale of x compact disc players isFind the marginal profit when x = 10 .

Group of answer choices

$239

$699

$230

$690

Flag question: Question 28Question 281pts

Solve the problem. A company estimates that the daily cost (in dollars) of producing x chocolate bars is given by Currently, the company produces 280 chocolate bars per day. Use marginal cost to estimate the increase in the daily cost if one additional chocolate bar is produced per day.

Group of answer choices

$0.32

$26.40

$32.00

$0.26

Flag question: Question 29Question 291pts

Solve the problem. A company estimates that the daily revenue (in dollars) from the sale of x cookies is given by Currently, the company sells 390 cookies per day. Use marginal revenue to estimate the increase in revenue if the company increases sales by one cookie per day.

Group of answer choices

$0.41

$48.80

$0.49

$41.00

Flag question: Question 30Question 301pts

Solve the problem. The average cost for a company to produce x thousand units of a product is given by the function A(x) = Use A'(x) to estimate the change in average cost if production is increased by one thousand units from the current level of 16 thousand.

Group of answer choices

Average cost will increase by $64

Average cost will decrease by $4

Average cost will increase by $4

Average cost will decrease by $64