Reference no: EM132956664

Question 1 Find the limit of the function shown below at x = 2:

options:

1

2

Not enough information to compute.

The limit does not exist.

Question 2 Find the limit of the function shown below at x = 5:

options:
Not enough information to compute.

1

3

The limit does not exist.

Question 3 Evaluate lim_x→3 x² - 9/x-3

options:

0

6

3

Not possible to calculate.

Question 4

Evaluate lim_x→3 (x² + 5x + 1)

15

3

Not possible to calculate.

25

Question 5

The function shown below is continuous at x = 2.

options:

True

false

Question 6

The function shown below is continuous at x = 3.

options:

True

false

Question 7 Determine if the piecewise defined function below is continuous at the origin.

options:

1) Not continuous

2) continuous

Question 8 To what new value should f(2) be changed in f(x) in order to remove the discontinuity?

options:

1) 13

2) 4

3) 7/8

4) 6

Question 9 Derivative of a function is the rate of change of that function with respect to one or more variables.

True

False

Question 10 Find the derivative of the function f(x) = 6x - 9, and calculate f'(2).

options:
1) f'(x) = -9; f'(2) = -9

2) f'(x) = 0; f'(2) = 0

3) f'(x) = 6; f'(2) = 6

4) f'(x) = 5x; f'(2) = 10

Question 11 Find the derivative of

4x^3-5x+6

options:

1) 12x2{"version":"1.1","math":"12x^2 "}

2) 12 x² - 5

3) 12x-5{"version":"1.1","math":"12x- 5"}

4) 4x2-5{"version":"1.1","math":"4x^2 - 5"}

Question 12

Find dy/dx if y(x) = 10 - 9x1/3

options:

1) -3x--√3{"version":"1.1","math":"-3\sqrt[3]{x}"}
2) 10-3x2--√3{"version":"1.1","math":"10-3\sqrt[3]{x^2}"}

3) -3/3√x²

Question 13 Find the derivative of s(t) = 3t² + 15t - 18

options:

2) 3t + 15

3) 3t2 + 15

4) 6t² + 15

Question 14 Find the slope of the function f(x)= 2x² -4x+3 at x = -2.

options:

1) 19

3) 4

4) -8

Question 15 Suppose the demand curve for some product was given by D(p)=1/p, where D is the quantity of items produced, in thousands, at a price of p dollars.

Interpret what the derivative of D represents at p = $3.

options:

D'(2) tells us that the demand of this product will increase by a ninth for every $1 of price increase.

D'(2) tells us that the demand of this product will decrease by a ninth for every $1 of price decrease.

D'(2) tells us that the demand of this product will increase by a ninth for every $1 of price decrease.

Question 16

Let  f(x) = 4x³

g(x) = 2x² + 5x

and

h(x) = 2f(x) - 4g(x).

Find

h'(2)

options:
0

96

44

-40

Question 17

For which values of x does

f(x)=6x^2+3x-1

has a tangent line of slope 15

options:

6

-2

1394

Question 18

The cost, in thousands of dollars, for producing x thousand tablet cases is given by C(x)= 1/250x² + x + 22

Find the value that best approximates the average cost when 10 thousand cases are produced.

options:

$22,000

$3.16

Not enough information given.

$31.4

Question 19

Find f'(x) if f(x) = (2x³+5x)²

options:

(2x³+5x)²(12x²+5)

6(2x²+5)

2(2x3+5x)

2(2x³+5x)(6x²+5)

Question 20

Consider the function

x -1 2 3 4 5 6 7
F(x) 10 15 18 20 23 26 30

Find the average rate of change of the function from x=4 to x=6

options:

3

-2

4

1