Question

\[\lim_{x\to 0}\frac{1-\cos(1-cosx)}{x^4}??????\]

Answer 1

Hi! I think you should divide the limit in two parts: x->0- and x->0+. Then, Have you tried De L'hospital until the denominator gets to 18?

Answer 2

+inf,use L'Hospital rule

Answer 3

\[\lim_{x \rightarrow 0} \frac {1-\cos(1-cosx)}{x^4} = \lim_{x \rightarrow 0}\frac {\sin(1-cosx).sinx}{4x^3}\]using l'hospitals.
\[\lim_{x \rightarrow 0} \frac {\sin(1-cosx)}{1-cosx}.\frac {2\sin ^2{x/2}}{16(\frac {x}{2})^2}.\ \frac {sinx}{x}\]=1/8