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Mathematics LibreTexts

2.4E: Infinite Limits EXERCISES

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2.4: Infinite Limit Exercises

In the following exercises, find the limit.

In the following exercises, consider the graph of the function y=f(x) shown here. Which of the statements about y=f(x) are true and which are false? Explain why a statement is false.

CNX_Calc_Figure_02_02_201.jpeg

J46) limx10f(x)=0

J47) limx2+f(x)=3

Answer:

False; limx2+f(x)=+

J48) limx8f(x)=f(8)

J49) limx6f(x)=5

Answer:

False; limx6f(x) DNE sincelimx6f(x)=2 and limx6+f(x)=5.

J2.4.1)

a. limx3+xx+3

b. limx3xx+3

c. limx3xx+3


Answer:
a. −∞
b. ∞
c. DNE

J2.4.2) limx0ln|x|

J2.4.3)

a. limx5+2x5

b. limx52x5

c. limx52x5

Answer:
a. ∞
b. −∞
c. DNE

J2.4.4)

a. limx2+x(x+2)2

b. limx2x(x+2)2

c. limx2x(x+2)2

J2.4.5)

a. limx6+x(6x)2

b. limx6x(6x)2

c. limx6x(6x)2

Answer:
a. ∞
b. ∞
c. ∞

J2.4.6)

a. limx1+2x2+7x4x2+x2

b. limx12x2+7x4x2+x2

c.limx12x2+7x4x2+x2

J2.4.7) limx1x31x21

Answer:
limx1x31x21=limx1(x1)(x2+x+1)(x1)(x+1)=limx1x2+x+1x+1=32

J2.4.8) limx1/22x2x1

J2.4.9) limx1/22x2+3x22x1

Answer:
limx1/22x2+3x22x1=limx1/2(2x1)(x+2)2x1=limx1/2(x+2)=52

State the vertical asymptote for each function, if any.

J2.4.10) f(x)=lnx

J2.4.11) g(x)=x+5x4

Answer:
x=4

J2.4.12) g(x)=7x+5

J2.4.13) g(x)=7x

Answer:
x=0

J2.4.14)

a. limxπ2+tanx=

b. limxπ2tanx=

c. limxπ2tanx=

d. Does f(x)=tanx have a vertical asymptote at x=π2?


2.4E: Infinite Limits EXERCISES is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.

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