Solving Homework Problems: Evaluating Limits of f(X) as X->0

[Lucy788]

hi I don't understand how to do one type of homework problem, here's an example of the type:
If limit of f(X)/X = 1 as X ->0 evaluate the limit f(X) as X->0

 

[Lucy788]

hi I don't understand how to do one type of homework problem, here's an example of the type:
If limit of f(X)/X = 1 as X ->0 evaluate the limit f(X) as X->0

I realize now that f(X) must equal X and therefor the limit is 0

 

[Samy_A]

hi I don't understand how to do one type of homework problem, here's an example of the type:
If limit of f(X)/X = 1 as X ->0 evaluate the limit f(X) as X->0

I realize now that f(X) must equal X and therefor the limit is 0

That's not a correct argument.

For example, $\displaystyle \lim_{x\rightarrow 0} \frac{\sin x}{x}=1$, but clearly $\sin x \neq x$ (for $x \neq 0$).

You could use the product rule for limits: $\displaystyle \lim_{x\rightarrow 0} g(x)h(x)=(\lim_{x\rightarrow 0} g(x))(\lim_{x\rightarrow 0} h(x))$ provided the limits exist.
Notice that $f(x)=x\frac{f(x)}{x}$.