Quiz about Calculus Review (limits, continuity, derivatives, integration)

Question 1

what is the derivative of y= sin(2x)?

Accepted Answer

y^/=2cos(2x)

Answer

y^/=cos(2x)

Answer

y^/=2sin(2x)

Answer

y^/=2sin(x)+cos(2x)

Question 2

What is the limit?

Accepted Answer

12

Answer

DNE

Answer

Infinity

Answer

6

Question 3

What is the limit?

Accepted Answer

20

Answer

Infinity

Answer

DNE

Answer

12

Question 4

What is the limit of the function as x approaches -4 from the left?

Accepted Answer

2

Answer

-4

Answer

DNE

Answer

-2

Question 5

Question 5.

Accepted Answer

DNE

Answer

-7

Answer

0

Answer

1

Question 6

Which of the following best describes the continuity at x = 1?

Accepted Answer

Removable Discontinuity

Answer

Continuous

Answer

Infinite Discontinuity

Answer

Jump Discontinuity

Question 7

What is the derivative of f(x) = 2x³- 4x + 5?

Accepted Answer

f'(x) = 6x² - 4

Answer

f'(x) = 6x² - 4x

Answer

f'(x) = 2/3x² - 4x

Answer

f'(x) = 3x² - 4

Question 8

What is the 2nd derivative of y = 2x³ - 4x + 6

Accepted Answer

12x

Answer

6x2 - 4

Answer

12x - 4

Answer

6x

Question 9

Does this function have an absolute maximum?

Accepted Answer

No

Answer

Yes

Question 10

When f'(x) changes from negative to positive, there is(are) ...

Accepted Answer

a minimum.

Answer

a maximum.

Answer

no extrema.

Question 11

When f'(x) changes from positive to negative, there is(are) ...

Accepted Answer

a maximum.

Answer

a minimum.

Answer

no extrema.

Question 12

Find the relative minimum values for f(x)=3x⁴-2x³-9x²

Accepted Answer

-1 and 1.5

Answer

-1

Answer

0

Answer

1.5

Question 13

The concavity of a function is described by its _______________.

Accepted Answer

second derivative

Answer

first derivative

Answer

third derivative

Answer

expression

Question 14

Identify the critical points of the following function:
g(x)=2x³-3x²

Accepted Answer

x=0,1

Answer

x=-1,1

Answer

x=0,0

Answer

x=0,-1

Question 15

What will be true at an inflection point?  (select the best answer)

Accepted Answer

f''(x)=0

Answer

f(x)=0

Answer

f'(x)=0

Answer

The function is undefined

Question 16

Find the derivative of f(x) = x²sinx

Accepted Answer

f'(x) = 2xsinx + x²cosx

Answer

f'(x) = 2xsinx - x²cosx

Answer

f'(x) = 2xsinx + x²sinx

Answer

f'(x) = 2xcosx

Question 17

Find the derivative of y = 2x² (3x - 4)

Accepted Answer

18x² - 16x

Answer

6x³ - 8x²

Answer

15x2 - 6x

Answer

6x - 4

Question 18

Find the derivative. $$y=\frac{x^2}{3x-1}$$

Accepted Answer

$$y$$

Answer

y' = 9x²- 12

Question 19

What is the derivative of sin(x)?

Accepted Answer

cos(x)

Answer

-sin(x)

Answer

-cos(x)

Answer

sin(x)

Question 20

What is the derivative of cos(x)?

Accepted Answer

-sin(x)

Answer

sin(x)

Answer

cos(x)

Answer

-cos(x)

Question 21

Given that $$y=\frac{x+2}{x-3}$$ , find y'.

Accepted Answer

$$y$$

Question 22

Where is the point of infection for the function $$y=x^3+6x^2$$ ?

Accepted Answer

-2

Answer

0

Answer

-4

Answer

4

Question 23

Find dy/dx $$xy+y^2=2$$

Accepted Answer

$$\frac{-y}{x+2y}$$

Answer

$$\frac{y}{x+2y}$$

Answer

$$\frac{-3y}{x}$$

Answer

$$\frac{-3x}{y}$$

Question 24

Which of the following functions would NOT be continuous?

Accepted Answer

y = 1/x

Answer

y = 5x

Answer

y = -x² + 6x

Answer

y = x3

Question 25

Find f'(0) if $$f\left(x\right)=\frac{5}{x-1}$$ .

Accepted Answer

-5

Answer

5

Answer

$$\frac{1}{5}$$

Answer

$$-\frac{1}{5}$$

Question 26

Find $$f$$ if $$f\left(x\right)=\sqrt[]{2x^2-5x}$$

Accepted Answer

$$\frac{4x-5}{2\ \sqrt[]{2x^2-5x}}$$

Answer

$$\frac{1}{\sqrt[]{4x-5}}$$

Answer

$$4x-5$$

Answer

$$\frac{1}{2\ \sqrt[]{2x^2-5x}}$$

Question 27

$$\int\left(x^2-2x\right)dx$$

Accepted Answer

$$\frac{1}{3}x^3-x^2+C$$

Answer

$$x^{2\ }-2x+C$$

Answer

$$2x-2$$

Answer

$$\frac{1}{3}x^3-x^2$$

Question 28

$$\int6x\left(x+2\right)dx$$

Accepted Answer

$$2x^3+6x^2+C$$

Answer

$$6x^2+12x+C$$

Answer

$$x^{2\ }-2x+C$$

Answer

$$3x^2+6x+C$$

Question 29

$$\int\left(5x^2-7x+6\right)dx$$

Accepted Answer

$$\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C$$

Answer

$$\frac{5}{3}x-\frac{7}{2}x+6x+C$$

Answer

$$x+x+x+x+x+C$$

Answer

$$x^3-3x^2+6x+C$$

Question 30

Accepted Answer

3

Answer

6

Answer

2

Answer

9

Question 31

Using the areas of each region given
$$\int_a^df\left(x\right)=$$

Accepted Answer

6

Answer

20

Answer

2

Answer

24

Question 32

Question 32.

Accepted Answer

0

Answer

Does Not Exist

Answer

9

Answer

1

Question 33

Find the limit. Hint: Where is the horizontal asymptote?

Accepted Answer

3/7

Answer

0

Answer

$$\infty$$

Answer

$$-\infty$$

Question 34

What is the average rate of change of the function $$f\left(x\right)\ =\ -\frac{1}{x+2}\ at\ the\ interval\ x\ =\ 0\ and\ x\ =\ 1?$$ Input in simplified fraction form.

Accepted Answer

1/6

Answer

-5/36

Answer

-1/6

Answer

5/36

Calculus Review (limits, continuity, derivatives, integration)

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