# Thread: Evaluating limit of cube root function algebraically

1. ## Evaluating limit of cube root function algebraically

Hello

I am having trouble evaluating the following problem

Lim cuberoot(sin8x/x)
x->0

It needs to be evaluated algebraically. I think it needs to be rationalized but I dont really know where to start

Any help is greatly appreciated. Sorry if this is the wrong forum

2. ## Re: Evaluating limit of cube root function algebraically

$\displaystyle \lim_{x \to 0} \sqrt[3]{ \dfrac{ \sin(8x) }{x} } = \sqrt[3]{ \displaystyle \lim_{x \to 0} \dfrac{ \sin(8x) }{x}} = \sqrt[3]{ \displaystyle 8\lim_{x \to 0} \dfrac{ \sin(8x) }{ 8x } } = \sqrt[3]{8\cdot 1} = 2$

3. ## Re: Evaluating limit of cube root function algebraically

SlipEternal has used
1) the fact that the cube root function is continuous.

2) the fact that the limit of sin(u)/u, as u goes to 0, is 1.