Evaluate the following limit : lim(x→0) (sin 2x(cos 3x - cos x))/x^3

Question

Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{sin\,2\text x(cos\,3\text x-cos\,\text x)}{\text x^3} \)

lim(x→0) (sin 2x(cos 3x - cos x))/x³

Answer 1

\(\lim\limits_{\text x \to0}\cfrac{sin\,2\text x(cos\,3\text x-cos\,\text x)}{\text x^3} \)

Since,

= -2(1 × 2) × 2 × 1

Hence, \(\lim\limits_{\text x \to0}\cfrac{sin\,2\text x(cos\,3\text x-cos\,\text x)}{\text x^3} \) = -8