Question 2: Which of the statements a through k about the function $y=f(x)$ graphed here are true, and which are false?

• The statement $\lim_{x \rightarrow 0} f(x)$ exists is:
• The statement $\lim_{x \rightarrow 0} f(x) =3$ is:
• The statement $lim_{x \rightarrow 0} f(x)=0$ is:
• The statement $lim_{x \rightarrow 2} f(x)=-2$ is
• The statement $lim_{x \rightarrow 2} f(x)=3$ is:
• The statement $lim_{x \rightarrow c} f(x)$ exists at every point c in (-1,2) is:
• The statement $lim_{x \rightarrow 2} f(x)$ does not exist is:
• The statement $f(0)=0$ is:
• The statement $f(0)=3$ is:
• The statement $f(2)=-2$ is:
• The statement $f(2)=3$ is:

Question 3: Explain why the limit does not exist.

$$ \lim_{x \, \rightarrow \, 0} \, \frac{x}{|x|} $$

Solution:

• As x approaches 0 from the left, $\frac{x}{|x|}$approaches -1. As x approaches 0 from the right, $\frac{x}{|x|}$ approaches 1?

Question 7: Find the following limit.

$$ \lim_{h \rightarrow 0} \, \frac{3}{\sqrt{3h+4}+4} $$

• Solution:

Question 10: Find the limit.

$$ \lim_{f \rightarrow 8} \frac{\frac{1}{f}-\frac{1}{8}}{f-8} $$

• Solution:

Question 13: Find

$$ \lim_{x \rightarrow -15} \frac{14-\sqrt{x^2-29}}{x+15} $$

• Solution: