Question

limit as x approaches 0 of (tan(4x))/(xsec(3x))

Answer 1

\[\large \lim_{x\to0} \frac{\tan 4x}{x\sec3x} \qquad\to\qquad \frac{0}{0\cdot1}\]

With the form that it's in now, this limit is approaching the indeterminate form 0/0.
In this form we're allowed to apply L'Hopital's Rule.
Have you learned L'Hop Yet?

Answer 2

you can devide the fraction by x
\[\lim_{x \rightarrow 0} \frac{ \frac{ \tan(4x) }{ x } }{ \frac{ x*\sec(3x) }{ x } }\]

\[\frac{ 4 }{ \sec0 } = 4\]