2.4E: Infinite Limits EXERCISES
( \newcommand{\kernel}{\mathrm{null}\,}\)
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.
J46) limx→10f(x)=0
J47) limx→−2+f(x)=3
- Answer:
-
False; limx→−2+f(x)=+∞
J48) limx→−8f(x)=f(−8)
J49) limx→6f(x)=5
- Answer:
-
False; limx→6f(x) DNE sincelimx→6−f(x)=2 and limx→6+f(x)=5.
J2.4.1)
a. limx→−3+xx+3
b. limx→−3−xx+3
c. limx→−3xx+3
- Answer:
- a. −∞
b. ∞
c. DNE
J2.4.2) limx→0ln|x|
J2.4.3)
a. limx→5+2x−5
b. limx→5−2x−5
c. limx→52x−5
- Answer:
- a. ∞
b. −∞
c. DNE
J2.4.4)
a. limx→−2+x(x+2)2
b. limx→−2−x(x+2)2
c. limx→−2x(x+2)2
J2.4.5)
a. limx→6+x(6−x)2
b. limx→6−x(6−x)2
c. limx→6x(6−x)2
- Answer:
- a. ∞
b. ∞
c. ∞
J2.4.6)
a. limx→1+2x2+7x−4x2+x−2
b. limx→1−2x2+7x−4x2+x−2
c.limx→12x2+7x−4x2+x−2
J2.4.7) limx→1x3−1x2−1
- Answer:
- limx→1x3−1x2−1=limx→1(x−1)(x2+x+1)(x−1)(x+1)=limx→1x2+x+1x+1=32
J2.4.8) limx→1/22x2x−1
J2.4.9) limx→1/22x2+3x−22x−1
- Answer:
- limx→1/22x2+3x−22x−1=limx→1/2(2x−1)(x+2)2x−1=limx→1/2(x+2)=52
State the vertical asymptote for each function, if any.
J2.4.10) f(x)=lnx
J2.4.11) g(x)=x+5x−4
- Answer:
- x=4
J2.4.12) g(x)=7x+5
J2.4.13) g(x)=7x
- Answer:
- x=0
J2.4.14)
a. limx→π2+tanx=
b. limx→π2−tanx=
c. limx→π2tanx=
d. Does f(x)=tanx have a vertical asymptote at x=π2?