calculus - Limits without L'Hopitals Rule

Evaluate the limit without using L'hopital's rule

a) $$\lim_{x \to 0} \frac {(1+2x)^{1/3}-1}{x}$$

I got the answer as $l=\frac 23$... but I used L'hopitals rule for that... How can I do it another way?

b) $$\lim_{x \to 5^-} \frac {e^x}{(x-5)^3}$$

$l=-\infty$

c) $$\lim_{x \to \frac {\pi} 2} \frac{\sin x}{\cos^2x} - \tan^2 x$$

I don't know how to work with this at all

So basically I was able to find most of the limits through L'Hopitals Rule... BUT how do I find the limits without using his rule?