Evaluate the following limit : lim(x→0) (sin^2 4x^2)/(x^4)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{sin^24\text x^2}{\text x^4} \)

lim(x→0) (sin² 4x²)/(x⁴)

Answer 1

To find: \(\lim\limits_{\text x \to0}\cfrac{sin^24\text x^2}{\text x^4} \)

\(\lim\limits_{\text x \to0}\cfrac{sin^24\text x^2}{\text x^4} \)

Therefore,

= 16 × (1)²

= 16

Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{sin^24\text x^2}{\text x^4} \) = 16