Evaluate the following limit : lim(x→0) (sin x^2(1 - cos x^2))/(x^6)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{sin\,\text x^2(1-cos\,\text x^2)}{\text x^6} \) 

lim(x→0) (sin x²(1 - cos x²))/(x⁶)

Answer 1

To find: \(\lim\limits_{\text x \to0}\cfrac{sin\,\text x^2(1-cos\,\text x^2)}{\text x^6} \)

We know,

cos 2x = 1 – 2 sin² x

Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{sin\,\text x^2(1-cos\,\text x^2)}{\text x^6} \) = \(\cfrac12\)