Question

\( \lim _{x \rightarrow 0} \frac{(1-\cos (1-\cos x))}{\sin ^{4} x} \)

Answer 1

We have

lim_(x→0) ((1 – cos(1 – cos x))/x⁴)

Answer 2

\({\lim\limits_{x \to 0} {(1-cos(1-cosx))\over x^4} } \)

\({\lim\limits_{x \to 0} {(1-cos(1-cosx))\over x^4} } *{(1-cosx)^2\over(1-cosx)^2}\)

\(\lim\limits_{x \to 0} {(1-cos(1-cosx))\over(1-cosx)^2}*{(1-cosx)^2\over (x^2)^2} \)

\(= {1 \over 2} * {1 \over 4} = {1 \over 8}\)