I need to evaluate
limx→0sin(4x)sin(3x)
I solved this using L'Hospital's Theorem and I got 4/3
However, is there a way to do this without applying this theoerm?
Answer
As \lim_{x \to 0}\frac{\sin(x)}{x}=1
\lim_{x \to 0}{\frac{\sin(4x)}{\sin(3x)}} can be written as
\frac{4}{3}\lim_{x \to 0}\frac{\sin(4x)}{4x}\frac{3x}{\sin(3x)}
=\frac{4}{3}
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