Originally Posted by
AlphaRock Thanks, o_O for answering.
I know how to solve limits numerically for these questions (Just put a number close to 0, eg. .0001), but I would like to know how to solve them algebraically:
1) lim ((2+x)^3 - 8)/x
x->0
Mr F says: Many approaches are possible. The least sophisticated is to expand the numerator and simplify. Then cancel the common factor. Then take the limit.
2) lim (sin x)/(2x^2-x)
x->0
Mr F says: Many approaches are possible. Here's one: $\displaystyle {\color{red} \frac{\sin x}{2x^2 - x} = \frac{\sin x}{x(2x-1)} = \frac{\sin x}{x} \, \frac{1}{2x-1}}$.
Now remember that the limit of a product is the product of the limits and recall $\displaystyle {\color{red}\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1}$.
I think we have to multiply 2x by lim and 2x by sin x, but am not really sure if it's right or what to do after...
3) lim (sin^2 x)/x
x->0
Mr F says: Consider the apporach in 2).
P.S. Tips or tricks for limits would be appreciated.