- #1
Hernaner28
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- 0
Homework Statement
Calculate: $$ \displaystyle \underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos \left( 1-\cos x \right)}{{{x}^{4}}}$$
Homework Equations
The Attempt at a Solution
Using Taylor series I have:
$$ \displaystyle f'\left( x \right)=\sin \left( 1-\cos x \right)\sin x$$
$$\displaystyle f'\left( 0 \right)=0$$
but as you can see, now it turns very tedious to continue differentiating. Do I have to keep differentiating until I get something? Or is there any quicker way to compute this?
Thanks