Question

limit as x approaches 0 of 3x-tan 7x all over 2x

Answer 1

\[\lim{x\to 0}\frac{3x-\tan7x}{2x}\\
\lim{x\to 0}\frac{3x}{2x}-\lim_{x\to 0}\frac{\tan7x}{2x}\]
The first is easy to deal with. The second limit can be written as
\[\frac{1}{2}\lim_{x\to 0}\large\frac{\frac{\sin x}{\cos x}}{x}\\
\frac{1}{2}\cdot\lim_{x\to 0}\frac{\sin x}{x}\cdot\lim_{x\to 0}\frac{1}{\cos x}\\
\]

Answer 2

You are a life saver thank you so much!