Question

1. 0 / 3.84 points find the limit. (if an answer does not exist, enter dne.) $lim_{x

ightarrow0}\frac{sin 6x}{x}$

Explanation:

Step1: Use limit - formula

We know the well - known limit $\lim_{u
ightarrow0}\frac{\sin u}{u}=1$. Let $u = 6x$. As $x
ightarrow0$, then $u = 6x
ightarrow0$.
We can rewrite $\lim_{x
ightarrow0}\frac{\sin6x}{x}$ as $\lim_{x
ightarrow0}\frac{\sin6x}{x}\times\frac{6}{6}=6\lim_{x
ightarrow0}\frac{\sin6x}{6x}$.

Step2: Substitute and find the limit

Since $\lim_{u
ightarrow0}\frac{\sin u}{u}=1$ and here $u = 6x$ (as $x
ightarrow0$, $u
ightarrow0$), we have $6\lim_{x
ightarrow0}\frac{\sin6x}{6x}=6\times1$.

Answer:

6