Calculating the Limit: $\lim_{x\to0}\frac{\sin x-x }{x^3}$

[MHD93]

Hi


Find the limit:
$$\lim_{x\to0}\frac{\sin x-x }{x^3}$$

 

[Mark44]

Hi


Find the limit:
$$\lim_{x\to0}\frac{\sin x-x }{x^3}$$

What have you tried?

 

[MHD93]

lim[x->0] (sinx - x)/x^3 = lim [x->0] sinx/x3 - 1/x2
but it's infinity - infinity!

 

[Mark44]

So that didn't do you any good.

Do you know about L'Hopital's Rule?

 

[hunt_mat]

Or the power series for sin x?