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(b) lim x→0 (sin(3x))/ (5x)

 

\(\displaystyle\lim_{x\rightarrow 0}\frac{ sin(3x)}{5x}\\ =\displaystyle\lim_{x\rightarrow 0}\frac{ sin(3x)}{3x\times \frac{5}{3}}\\ =\displaystyle\lim_{x\rightarrow 0}\frac{ sin(3x)}{3x}\times \frac{3}{5}\\ =1 \times \frac{3}{5}\\ =\frac{3}{5}\\\)

A note to answerers.

 

Don't bother with the first question as the poster has already reposted it!