Question

limit of f(x) given by f(x)=(1-cosx)/x^2*cos4x, x->0

Answer 1

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Answer 2

Help?

Answer 3

great, now i dont want to give you my answer cuase its prolly wrong

Answer 4

\[\lim_{x\rightarrow 0}\frac{1-\cos{x}}{x^2\cdot\cos{4x}}=
\underbrace{\lim_{x\rightarrow 0}\frac{1}{\cos{4x}}}_{=1}\cdot\lim_{x\rightarrow 0}\frac{1-\cos{x}}{x^2}=\lim_{x\rightarrow 0}\frac{1-\cos{x}}{x^2}=\]
\[=\lim_{x\rightarrow 0}\frac{\sin{x}}{2x}=\lim_{x\rightarrow 0}\frac{\cos{x}}{2}=\frac{1}{2}\]