Answer
a. True,
b. False,
c. False,
d. True,
e. True,
f. True,
g. True,
h. True,
i. True,
j. False,
k. True,
Work Step by Step
Based on the graph given in the Exercise:
a. True, because when $x$ approaches $-1$ from the right-side, $f(x)\to 1$
b. False, $\lim_{x\to2}f(x)=1$ because the left and right side limits are equal.
c. False, $\lim_{x\to2}f(x)=1$ because the left and right side limits are equal to $1$.
d. True, because when $x$ approaches $1$ from the left-side, $f(x)\to 2$
e. True, because when $x$ approaches $1$ from the right-side, $f(x)\to 1$
f. True, because the left and right side limits are not equal.
g. True, because the left and right side limits are equal to $0$.
h. True, in the open interval $(-1,1)$, every point has a limit.
i. True, in the open interval $(1,3)$, every point has a limit.
j. False, the function to the left-side of point $x=-1$ is undefined.
k. True, the function to the right-side of point $x=3$ is undefined.
