2.4E: Infinite Limits EXERCISES
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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) \displaystyle \lim_{x→10}f(x)=0
J47) \displaystyle \lim_{x→−2^+}f(x)=3
False; \displaystyle \lim_{x→−2^+}f(x)=+∞
J48) \displaystyle \lim_{x→−8}f(x)=f(−8)
J49) \displaystyle \lim_{x→6}f(x)=5
False; \displaystyle \lim_{x→6}f(x) DNE since\displaystyle \lim_{x→6^−}f(x)=2 and \displaystyle \lim_{x→6^+}f(x)=5.
J2.4.1)
a. \displaystyle \lim_{x→−3^+}\frac{x}{x+3}
b. \displaystyle \lim_{x→−3^-}\frac{x}{x+3}
c. \displaystyle \lim_{x→−3}\frac{x}{x+3}
J2.4.2) \displaystyle \lim_{x→0}\ln |x|
J2.4.3)
a. \displaystyle \lim_{x→5^+}\frac{2}{x-5}
b. \displaystyle \lim_{x→5^-}\frac{2}{x-5}
c. \displaystyle \lim_{x→5}\frac{2}{x-5}
J2.4.4)
a. \displaystyle \lim_{x→-2^+}\frac{x}{(x+2)^2}
b. \displaystyle \lim_{x→-2^-}\frac{x}{(x+2)^2}
c. \displaystyle \lim_{x→-2}\frac{x}{(x+2)^2}
J2.4.5)
a. \displaystyle \lim_{x→6^+}\frac{x}{(6-x)^2}
b. \displaystyle \lim_{x→6^-}\frac{x}{(6-x)^2}
c. \displaystyle \lim_{x→6}\frac{x}{(6-x)^2}
J2.4.6)
a. \displaystyle \lim_{x→1^+}\frac{2x^2+7x−4}{x^2+x−2}
b. \displaystyle \lim_{x→1^−}\frac{2x^2+7x−4}{x^2+x−2}
c.\displaystyle \lim_{x→1}\frac{2x^2+7x−4}{x^2+x−2}
J2.4.7) \displaystyle \lim_{x→1}\frac{x^3−1}{x^2−1}
J2.4.8) \displaystyle \lim_{x→1/2}\frac{2x}{2x−1}
J2.4.9) \displaystyle \lim_{x→1/2}\frac{2x^2+3x−2}{2x−1}
State the vertical asymptote for each function, if any.
J2.4.10) f(x)=\ln x
J2.4.11) g(x)=\frac{x+5}{x-4}
J2.4.12) g(x)=\frac{7}{x+5}
J2.4.13) g(x)=\frac{7}{x}
J2.4.14)
a. \displaystyle \lim_{x→\frac{\pi}{2}^+}\tan x=
b. \displaystyle \lim_{x→\frac{\pi}{2}^-}\tan x=
c. \displaystyle \lim_{x→\frac{\pi}{2}}\tan x=
d. Does f(x)=\tan x have a vertical asymptote at x=\frac{\pi}{2}?