Free Printable Review for Quiz 3

1.

Evaluate the following limit

\lim_{x\rightarrow0}\left(\frac{\sin\left(3x\right)}{2x}\right)

a)

3/2

b)

2/3

c)

2

d)

3

e)

DNE

2.

What is the derivative of f(x) if

f\left(x\right)=2x+1

(a)

3.

Evaluate the following limit:

\lim_{x\rightarrow\infty}\frac{5x^{2\ }+3x-1}{x+2}

a)

$\infty$

b)

$-\infty$

c)

5

d)

0

e)

DNE

4.

What is the average rate of change of

f\left(x\right)=x^{4\ }-5x

on

\left[0,\ 3\right]

a)

8.5

b)

8.7

c)

22

d)

33

e)

66

5.

If $\lim_{x\rightarrow3}\ \ f\left(x\right)=7$ which must be true?
I. f is continuous at x =3
II. f(3)=7

a)

I

b)

II

c)

I and II

d)

Neither

6.

Use the limit definition of the derivative to calculate the derivative of $f\left(x\right)=3x^2$ evaluated at x = 4

a)

1

b)

48

c)

24

d)

0

7.

Write the equation of the normal line to the function $f\left(x\right)=5x^2+5x$ at $x=1$

a)

$y-10=-\frac{1}{15}\left(x-1\right)$

b)

$y-1=\frac{1}{15}\left(x-10\right)$

c)

$y-10=15\left(x-1\right)$

d)

$y-10=\frac{1}{15}\left(x-1\right)$

8.

The following limit equation is equivalent to which of the following?

$\lim_{x\rightarrow3}\frac{f\left(x\right)-f\left(3\right)}{x-3}=2$

a)

$f'\left(3\right)=2$

b)

$f\left(3\right)=2$

c)

$f\left(2\right)=3$

d)

$f'\left(2\right)=3$

9.

Which of the following is a way to notate the instantaneous rate of change of N(t) at t = 5?

a)

N(5)

b)

N'(5)

c)

N''(5)

d)

N(t)=5

10.

A student attempted to confirm that $f\left(x\right)=\frac{x^2+x+6}{x^2-7x+10}$

is continuous at x=2. Which step, if any, does an error first appear?

a)

Step 1

b)

Step 2

c)

Step 3

d)

Step 4

e)

There is no error

11.

The function g is continuous at all x-values except at x = 4. If $\lim_{x\rightarrow4}\ g\left(x\right)=\infty$

which of the following must be true regarding g(x)?

a)

There is a horizontal asymptote at y = 4

b)

There is a vertical asymptote at x = 4

c)

There is a hole at x = 4

d)

There is an x-intercept at x = 4

e)

There is a jump discontinuity at x = 4

12.

The amount of gasoline in a storage tank at time t is given by the function G(t). Selected values of this are shown in the table above. Use the data to estimate the rate of change of the amount of gasoline at t=3 hours.

a)

0.25 thousand gallons/hour

b)

0.5 thousand gallons/hour

c)

18.5 thousand gallons/hour

d)

19.5 thousand gallons/hour

13.

Find the instantaneous rate of change (i.e. the derivative) of f(x)=4x² at any point, x, using the limit definition of the derivative.

a)

$f'\left(x\right)=4x^{2\ }$

b)

$f'\left(x\right)=0$

c)

$f'\left(x\right)=8x$

d)

$f'\left(x\right)=4x+2$

Review for Quiz 3

Total questions: 13

Worksheet time: 7mins

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