How do you find the limit of $\frac{{sin}^{2} (x^{2})}{x^{4}}$ $(sin^2(x^2))/(x^4)$ as x approaches 0?

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Answer 1 · 2016-03-03T18:52:06

$1$ $1$

Let $f (x) = \frac{{sin}^{2} (x^{2})}{x^{4}}$ $f(x)=(sin^2(x^2))/x^4$

$implies f'(x)=lim_(x to 0) (sin^2(x^2))/x^4$

$implies f'(x)=lim_(x to 0) (sin(x^2)*sin(x^2))/x^4=lim_(x to 0) {sin(x^2)/x^2*sin(x^2)/x^2}=lim_(x to 0)sin(x^2)/x^2lim_(x to 0)sin(x^2)/x^2*=1*1=1$

How do you find the limit of (sin^2(x^2))/(x^4)sin2(x2)x4 (sin^2(x^2))/(x^4) as x approaches 0?