Question 1

Find:  $\lim_{x\rightarrow4}\frac{x^2  - 2x - 8}{x^2 - 16}$ if it exists.

Accepted Answer

$\frac{3}{4}$

Answer

0

Answer

$\infty$

Answer

DNE

Question 2

What type of discontinuity does this graph have at x = 2?

Accepted Answer

Removable discontinuity

Answer

Jump Discontinuity

Answer

Infinite Discontinuity

Answer

Non-removable discontinuity

Question 3

What is the limit as x approaches 2 of the graph shown?

Accepted Answer

4

Answer

$\infty$

Answer

The limit does not exist

Answer

2

Question 4

Is f(x) continuous at x = 1?

Accepted Answer

Yes, the 3 criteria of continuity at a point are met.

Answer

No, f(1) $
eq$ $\lim_{xightarrow1}f(x)$

Answer

Yes, because f(1) = 1

Answer

No, $\lim_{x\rightarrow1} f(x)= DNE$ because the left and right-hand limits are not equal.

Question 5

What are the asymptotes of f(x)?

Accepted Answer

Horizontal asymptote at y = 1 and a vertical asymptote at x = 4.

Answer

Horizontal asymptote at y = 1 and two vertical asymptotes at x = 4, -2.

Answer

No Horizontal asymptote and vertical asymptote at x = 4.

Answer

No Horizontal asymptote and two vertical asymptotes at x = 4, -2.

Question 6

The graph of the derivative of f(x) is shown.  At what x-value(s) does f(x) have a relative maximum?

Accepted Answer

f(x) has a relative maximum at x = -2

Answer

f(x) has a relative maximum at x = 1

Answer

f(x) does not have a relative maximum

Question 7

If we know the information shown, what can we also conclude?

Accepted Answer

f'(3) = 5

Answer

f is not continuous at x = 3

Answer

f'(5) = 3

Answer

$\lim_{x\rightarrow3}f(x) = 5$

Question 8

The position of a particle moving along a horizontal line is given by the function $s(t) = t^3 - 23t^2 + 120t$, where s is measured in meters and t is seconds.  What is the velocity of the object at t = 2 seconds?

Accepted Answer

40 m/s

Answer

-34 m/s

Answer

0 m/s

Answer

156 m/s

Question 9

If $xy + y^2 - 3x = 4x + 1$ find $\frac{dy}{dx}$.

Accepted Answer

$\frac{dy}{dx} = \frac{7-y}{x+2y}$

Answer

$\frac{dy}{dx} = \frac{7}{3}$

Answer

$\frac{dy}{dx} = \frac{7-y}{2y}$

Answer

$\frac{dy}{dx} = \frac{-y}{x+2y}$

Question 10

A block of ice, in the shape of a right circular cone, is melting in such a way that both its height and its radius r are decreasing at the rate of  1 cm/hr.  How fast is the volume decreasing when r = h = 10 cm?     $V_{cone} = \frac{1}{3}\pi r^2h$

Accepted Answer

-100$\pi$ $cm^3/hr$

Answer

1000$\pi$ $cm^3/hr$

Answer

100$\pi$ $cm^3/hr$

Answer

-1000$\pi$ $cm^3/hr$

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