Question

functions h and f are graphed. find lim(x→ - 1) h(x)/f(x).

Explanation:

Step1: Find $\lim_{x

ightarrow - 1}h(x)$
As $x$ approaches $-1$ from both the left - hand side and the right - hand side of the graph of $y = h(x)$, $h(x)$ approaches $1$. So, $\lim_{x
ightarrow - 1}h(x)=1$.

Step2: Find $\lim_{x

ightarrow - 1}f(x)$
As $x$ approaches $-1$ from both the left - hand side and the right - hand side of the graph of $y = f(x)$, $f(x)$ approaches $0$. So, $\lim_{x
ightarrow - 1}f(x)=0$.

Step3: Use the limit quotient rule

The limit quotient rule states that $\lim_{x
ightarrow a}\frac{h(x)}{f(x)}=\frac{\lim_{x
ightarrow a}h(x)}{\lim_{x
ightarrow a}f(x)}$ (when $\lim_{x
ightarrow a}f(x)
eq0$). Here, since $\lim_{x
ightarrow - 1}f(x) = 0$ and $\lim_{x
ightarrow - 1}h(x)=1$, the limit $\lim_{x
ightarrow - 1}\frac{h(x)}{f(x)}$ does not exist (DNE) because we have a non - zero number divided by zero.

Answer:

DNE