Question

find the limit.
lim(θ→0)(sin3x/(5x^3-4x)

Answer 1

Do you mean\[\lim_{\theta\to0}\frac{\sin3\theta}{5\theta^3-4\theta}\]

Answer 2

There is no theta

Answer 3

yes i do mean theat

Answer 4

*theta

Answer 5

\[\begin{align*}\lim_{\theta\to0}\frac{\sin3\theta}{5\theta^3-4\theta}&=\lim_{\theta\to0}\frac{\sin3\theta}{\theta(5\theta^2-4)}\\
&=\lim_{\theta\to0}\frac{3\sin3\theta}{3\theta(5\theta^2-4)}\\
&=\lim_{\theta\to0}\frac{\sin3\theta}{3\theta}\cdot\lim_{\theta\to0}\frac{3}{5\theta^2-4}
\end{align*}\]