Question

${lim}_{x\to 0}\frac{3sinx-4si{n}^{3}x}{x}$

Answer 1

${lim}_{x\to 0}\frac{3sinx-4si{n}^{3}x}{x}$

$={lim}_{x\to 0}\frac{sin3x}{x}[\because sin3x=3sinx-4si{n}^{3}x]$

$={lim}_{x\to 0}\frac{sin3x}{x}\times 3=3\times {lim}_{x\to 0}\frac{sin3x}{x}$

$=3\times {lim}_{x\to 0}\frac{sin3x}{3x}[\because x\to 0,3x\to 0]$

$=3\times 1[\because {lim}_{x\to 0}\frac{sinx}{x}=1]$

=3