Complete the table and use the result to estimate the limit. $\lim _ { x \rightarrow 0 } \frac { \sin ^ { 3 } x } { x ^ { 3 } }$$\begin{array}{|c|c|c|c|c|c|c|}
\hline x & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \
\hline f(x) & & & & & & \
\hline
\end{array}$
A) $- 0.5$
B) 0
C) 1
D) $0.5$
E) $- 1$

Question

Quizplus · Accepted Answer

The limit $\lim _ { x \rightarrow 0 } \frac { \sin ^ { 3 } x } { x ^ { 3 }}$ approaches 1 as $x$ approaches 0. This is because the limit of $\frac{\sin x}{x}$ as $x$ approaches 0 is 1, and this property holds for the cube of the function as well.

Complete the Table and Use the Result to Estimate the Limit