Question

Evaluate the limit:

$\underset{x\to 0}{lim}\frac{si{n}^{2}4x^2}{x^4}$

Answer 1

We have,

$\underset{x\to 0}{lim}\frac{si{n}^{2}4x^2}{x^4}$

It becomes 0/0 form.

$=\underset{x\to 0}{lim}\frac{sin4x^2}{4x^2}\times \frac{sin4x^2}{4x^2}\times 16[\because \underset{x\to 0}{lim}\frac{sinx}{x}=1]$

$=1\times 1\times 16$

$=16$

Therefore,

$\underset{x\to 0}{lim}\frac{si{n}^{2}4x^2}{x^4}=16$