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Advanced Calculus QBA #2

Total questions: 25

Worksheet time: 2hrs 5mins

Name
Class
Date
1.

Find the limit: limx5(2x+1)\lim_{x\rightarrow5}\left(2x+1\right) .

a)

5

b)

11

c)

1

d)

DNE

2.

Find the limit: limx2 x24x2\lim_{x\rightarrow2}\ \frac{x^2-4}{x-2}

a)

4

b)

-2

c)

-4

d)

0

3.

Find the limit: limx4 3\lim_{x\rightarrow4}\ 3

a)

4

b)

3

c)

12

d)

DNE

4.

Find the limit: limx4 x4x2\lim_{x\rightarrow4}\ \frac{x-4}{\sqrt[]{x}-2}

a)

0

b)

4

c)

12\frac{1}{2}

d)

DNE

5.

Find the limit: limx(2) x32x25x+6x+2\lim_{x\rightarrow\left(-2\right)}\ \frac{x^3-2x^2-5x+6}{x+2}

a)

-1

b)

15

c)

0

d)

DNE

6.

Find the limit: limx3 2x3\lim_{x\rightarrow3}\ \frac{2}{x-3}

a)

+∞

b)

-∞

c)

0

d)

DNE

7.

Find the limit: limx 2xx1\lim_{x\rightarrow\infty}\ \frac{2x}{x-1}

a)

2

b)

1/2

c)

0

d)

DNE

8.

Find the limit: limx() x1x2+2x5\lim_{x\rightarrow\left(-\infty\right)}\ \frac{x-1}{x^2+2x-5}

a)

1

b)

-1

c)

0

d)

DNE

9.

Using the graph, what is limx2 f(x)\lim_{x\rightarrow2}\ f\left(x\right) ?

a)

1

b)

0

c)

2

d)

5

10.

Using the graph, what is limx f(x)\lim_{x\rightarrow\infty}\ f\left(x\right) ?

a)

++\infty

b)

-\infty

c)

0

d)

DNE

11.

Using the graph, what is limx() f(x)\lim_{x\rightarrow\left(-\infty\right)}\ f\left(x\right) ?

a)

++\infty

b)

-\infty

c)

0

d)

DNE

12.

What is the limx(3) f(x)\lim_{x\rightarrow\left(3^-\right)}\ f\left(x\right) ?

a)

1

b)

-1

c)

0

d)

DNE

13.

What is the limx(3+) f(x)\lim_{x\rightarrow\left(3^+\right)}\ f\left(x\right) ?

a)

1

b)

-1

c)

0

d)

DNE

14.

What is the limx3 f(x)\lim_{x\rightarrow3}\ f\left(x\right) ?

a)

1

b)

-1

c)

0

d)

DNE

15.

What is the limx(2) f(x)\lim_{x\rightarrow\left(2^-\right)}\ f\left(x\right) ?

a)

++\infty

b)

-\infty

c)

0

d)

DNE

16.

What is the limx(2+) f(x)\lim_{x\rightarrow\left(2^+\right)}\ f\left(x\right) ?

a)

++\infty

b)

-\infty

c)

0

d)

DNE

17.

What is the limx2 f(x)\lim_{x\rightarrow2}\ f\left(x\right) ?

a)

++\infty

b)

-\infty

c)

0

d)

DNE

18.

Name the type of discontinuity for the graph of f(x)=x29x+3f\left(x\right)=\frac{x^2-9}{x+3} .

a)

infinite

b)

jump

c)

point

d)

none

19.

Name the type of discontinuity for the graph of f(x) given to the left.

a)

infinite

b)

jump

c)

point

d)

none

20.

Name the type of discontinuity for the graph of f(x)=1x2f\left(x\right)=\frac{1}{x-2} .

a)

infinite

b)

jump

c)

point

d)

none

21.

For f(x)=x25f\left(x\right)=x^2-5 find the slope of the secant line over the interval [-1, 2].

a)

-5

b)

2

c)

1

d)

-2

22.

For f(x)=x25f\left(x\right)=x^2-5 find the slope of the tangent line at x = -1.

a)

A) -5

b)

B) 2

c)

C) 1

d)

D) -2

23.

For f(x)=x25f\left(x\right)=x^2-5 find the equation of the tangent line at x = -1.

a)

A) y = -5x + 1

b)

B) y = 2x - 2

c)

C) y = 1x -3

d)

D) y = -2x - 6

24.

For f(x)=x25f\left(x\right)=x^2-5 find the derivative at a general point.

a)

A) 2x

b)

B) -5x

c)

C) x - 5

d)

D) x²

25.

A __________ is a line that hits the edge of a curve at one point.

a)
A) tangent line
b)
B) secant line
c)
C) derivative
d)
D) parallel line