Calculus HW #3

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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 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 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)

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: • •

(incorrect)

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