f(x) and g(x) are differentiable on 0(adsbygoogle = window.adsbygoogle || []).push({});

f(0)=g(0)=0

[tex]

\lim _{x->0}\frac{cos(f(x))-cos(g(x))}{x^2}=\lim _{x->0}\frac{-2sin(\frac{f(x)+g(x)}{2})sin(\frac{f(x)-g(x)}{2})}{x^2}=-2

[/tex]

because i can use (sin x)/x=1 here

is it ok??

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# Limit of differentiable functions question

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