Kyle Taitt CSU WebworkMATH 160 WeBWorK assignment M160-801-F.docx

Kyle Taitt CSU Webwork
MATH 160 WeBWorK assignment M160-801-FA-1.3 due 09/07/2016 at 11:59pm MDT

1. (1 point) Evaluate the following limits:

1. lim
x→∞

5x3 −5x2 −5x
6−4x−2x3

=

2. lim
x→−∞

5x3 −5x2 −5x
6−4x−2x3

=

Answer(s) submitted:

•
•

(incorrect)

2. (1 point) Evaluate

lim
x→∞
−4x6 + 7x3 −5.

Limit =
Answer(s) submitted:

•
(incorrect)

3. (1 point)
A function is said to have a horizontal asymptote if either the
limit at infinity exists or the limit at negative infinity exists.
Show that each of the following functions has a horizontal
asymptote by calculating the given limit.

lim
x→∞

−13x
12 + 2x

=

lim
x→−∞

12x−9
x3 + 2x−15

=

lim
x→∞

x2 −14x−7
4−6x2

=

lim
x→∞

√
x2 + 15x
4−7x

=

lim
x→−∞

√
x2 + 15x
4−7x

=

Answer(s) submitted:

•
•
•
•
•

(incorrect)

4. (1 point) Evaluate

lim
x→∞

√
x4 + 3x3 −6
10x2 + 6

Answer(s) submitted:

•

(incorrect)

5. (1 point) Find the horizontal limit(s) of the following func-
tion:

f (x) =
6x3 −3x2 −3x
8−6x−4x3

and

Answer(s) submitted:

•
•

(incorrect)

6. (1 point) Evaluate the limit

lim
x→∞

(6−x)(8 + 3x)
(3−9x)(2 + 8x)

Answer(s) submitted:

•
(incorrect)

7. (1 point)
Evaluate the following limits. If needed, enter ’INF’ for ∞

and ’-INF for −∞.
(a)

lim
x→∞

√
6 + 5x2

4 + 11x
=

(b)

lim
x→−∞

√
6 + 5x2

4 + 11x
=

Answer(s) submitted:

•
•

(incorrect)

8. (1 point)
Evaluate the following limit. If the answer is positive infinite,

type ”I”; if negative infinite, type ”N”; and if it does not exist,
type ”D”.

lim
x→∞

x + x3 + x5

1−x2 + x4

Answer(s) submitted:

•
(incorrect)

1



9. (1 point) Evaluate the following limit.

lim
x→∞

x4 −4x2 + 2
x5 + 3x3

Answer:
Answer(s) submitted:

•

(incorrect)

10. (1 point) Evaluate the following limits:

1. lim
x→5

2
(x−5)6

=

2. lim
x→−7−

1
x2(x + 7)

=

3. lim
x→3−

2
x−3

=

4. lim
x→5−

2
(x−5)3

=

Answer(s) submitted:

•
•
•
•

(incorrect)

11. (1 point) This problem has two parts. The second part
will appear after you answer the first part correctly.

(a) What are the vertical asymptotes of f (x) =
4x2

x2 −49
? Your

answer should be a number, a list of numbers separated by com-
mas, or None .

Vertical asymptotes at x =

Answer(s) submitted:

•

(incorrect)

12. (1 point) Find the following limit.

lim
x→−8−

x + 3
x + 8

Limit: help (limits)
Answer(s) submitted:

•

(incorrect)

13. (1 point) Evaluate lim
x→0

x−3
x2(x−2)

Limit = help (limits)
Answer(s) submitted:
•

(incorrect)

14. (1 point)

Find the horizontal and vertical asymptotes of each curve.
List them in increasing order. If there is no such asymptote,
enter ”N”.

y =
x3

x2 + 3x−10

x =
x =
y =

Answer(s) submitted:
•
•
•

(incorrect)

15. (1 point) Let f (x) be a function such that

lim
x→∞

f (x) = ∞ lim
x→−∞

f (x) = 7

lim
x→7+

f (x) = ∞ lim
x→7−

f (x) =−∞

Determine the horizontal asymptote.

y =

Determine the vertical asymptote.
x =

Answer(s) submitted:
•
•

(incorrect)

16. (1 point) Let

f (x) =
x2 + 3x−10

3x2 + 13x−10
.

Find the horizontal ...

1. Kyle Taitt CSU Webwork
MATH 160 WeBWorK assignment M160 -801-FA-1.3 due
09/07/2016 at 11:59pm MDT

1. (1 point) Evaluate the following limits:

1. lim
x→∞

5x3 −5x2 −5x
6−4x−2x3

=

2. lim
x→−∞

5x3 −5x2 −5x
6−4x−2x3

=

Answer(s) submitted:

•
•

(incorrect)

2. (1 point) Evaluate

lim

2. x→∞
−4x6 + 7x3 −5.

Limit =
Answer(s) submitted:

•
(incorrect)

3. (1 point)
A function is said to have a horizontal asymptote if either the
limit at infinity exists or the limit at negative infinity exists.
Show that each of the following functions has a horizontal
asymptote by calculating the given limit.

lim
x→∞

−13x
12 + 2x

=

lim
x→−∞

12x−9
x3 + 2x−15

=

lim
x→∞

x2 −14x−7
4−6x2

3. =

lim
x→∞

√
x2 + 15x
4−7x

=

lim
x→−∞

√
x2 + 15x
4−7x

=

Answer(s) submitted:

•
•
•
•
•

(incorrect)

4. (1 point) Evaluate

lim
x→∞

4. √
x4 + 3x3 −6
10x2 + 6

Answer(s) submitted:

•

(incorrect)

5. (1 point) Find the horizontal limit(s) of the following func-
tion:

f (x) =
6x3 −3x2 −3x
8−6x−4x3

and

Answer(s) submitted:

•
•

(incorrect)

6. (1 point) Evaluate the limit

lim
x→∞

(6−x)(8 + 3x)
(3−9x)(2 + 8x)

Answer(s) submitted:

5. •
(incorrect)

7. (1 point)
Evaluate the following limits. If needed, enter ’INF’ for ∞

and ’-INF for −∞.
(a)

lim
x→∞

√
6 + 5x2

4 + 11x
=

(b)

lim
x→−∞

√
6 + 5x2

4 + 11x
=

Answer(s) submitted:

•
•

(incorrect)

6. 8. (1 point)
Evaluate the following limit. If the answer is positive infinite,

type ”I”; if negative infinite, type ”N”; and if it does not exist,
type ”D”.

lim
x→∞

x + x3 + x5

1−x2 + x4

Answer(s) submitted:

•
(incorrect)

1



9. (1 point) Evaluate the following limit.

lim
x→∞

x4 −4x2 + 2
x5 + 3x3

Answer:
Answer(s) submitted:

•

(incorrect)

7. 10. (1 point) Evaluate the following limits:

1. lim
x→5

2
(x−5)6

=

2. lim
x→−7−

1
x2(x + 7)

=

3. lim
x→3−

2
x−3

=

4. lim
x→5−

2
(x−5)3

=

Answer(s) submitted:

8. •
•
•
•

(incorrect)

11. (1 point) This problem has two parts. The second part
will appear after you answer the first part correctly.

(a) What are the vertical asymptotes of f (x) =
4x2

x2 −49
? Your

answer should be a number, a list of numbers separated by com-
mas, or None .

Vertical asymptotes at x =

Answer(s) submitted:

•

(incorrect)

12. (1 point) Find the following limit.

lim
x→−8−

x + 3
x + 8

9. Limit: help (limits)
Answer(s) submitted:

•

(incorrect)

13. (1 point) Evaluate lim
x→0

x−3
x2(x−2)

Limit = help (limits)
Answer(s) submitted:
•

(incorrect)

14. (1 point)

Find the horizontal and vertical asymptotes of each curve.
List them in increasing order. If there is no such asymptote,
enter ”N”.

y =
x3

x2 + 3x−10

x =
x =
y =

Answer(s) submitted:
•

10. •
•

(incorrect)

15. (1 point) Let f (x) be a function such that

lim
x→∞

f (x) = ∞ lim
x→−∞

f (x) = 7

lim
x→7+

f (x) = ∞ lim
x→7−

f (x) =−∞

Determine the horizontal asymptote.

y =

Determine the vertical asymptote.
x =

Answer(s) submitted:
•
•

(incorrect)

11. 16. (1 point) Let

f (x) =
x2 + 3x−10

3x2 + 13x−10
.

Find the horizontal and vertical asymptotes of f (x). If there are
no asymptotes of a given type, enter ’none’. If there are more
than one of a given type, list them separated by commas.

Horizontal asymptote(s): y =
2



Vertical asymptote(s): x =

Answer(s) submitted:

•
•

(incorrect)

17. (1 point) Let

f (x) =
x6

x2 + 3
.

Find the equations of the horizontal asymptotes and the ver-
tical asymptotes of f (x). If there are no asymptotes of a given

12. type, enter ’NONE’. If there is more than one asymptote of a
given type, give a comma separated list (i.e.: 1, 2,...).
Horizontal asymptotes: y =

Vertical asymptotes: x =

Answer(s) submitted:

•
•

(incorrect)

18. (1 point) Let

f (x) =
x + 5
2x2

.

Find the equations of the horizontal asymptotes and the vertical
asymptotes of f (x). If there are no asymptotes of a given type,
enter ’NONE’. If there is more than one asymptote of a given
type, give a comma separated list (i.e.: 1, 2,...).
Horizontal asymptotes: y =

Vertical Asymptotes: x =
Answer(s) submitted:
•
•

(incorrect)

19. (1 point)

13. Find lim
x→∞

f (x) if
4x−1

x
< f (x) <

4x2 + 3x
x2

for all x > 5.

Answer(s) submitted:
•

(incorrect)

20. (1 point) Suppose

7x−34 ≤ f (x)≤ x2 −x−18

Use this to compute the following limit.

lim
x→4

f (x)

Answer:

What theorem did you use to arrive at your answer?
Answer:

Answer(s) submitted:

14. •
•

(incorrect)

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Mathematical Association of America

3


Assignment 2: It May Not Work in Politics
Write a three page paper in which the student addresses the
following three (3) items using headers to separate each
response:
1. Congressional Ethics. Identify one (1) member of Congress
who has been charged with ethics violations. Briefly discuss the
reason for the charges and provide two (2) reasons why you
agree or disagree with the verdict and any penalties. Provide
examples to support your answer. Note: Consider how the
verdict and penalties impacts your trust of the members of
Congress.
2. Third Party Candidates. Discuss two (2) political reasons
why a third party candidate has never been successful in
winning a presidential election. Provide examples to support the
answer. Note: Consider the political impact of the Republican
and Democratic Party if a third party was successful.
3. Federal and State Authority. Identify one (1) current issue
facing the United States today. Analyze the respective roles of
Federal and state authorities in addressing the issue. Determine
whether the U. S. Constitution constrains the Federal and state
responses to the issue. Explain.

4. APA FORMAT