Hey all, just doing some homework in preparation for the quiz tomorrow (well, today...it's in 4 hours).

Running into trouble with using limits to compute derivatives.

Here are the problems:

Use limits to compute the following derivatives:

1. $\displaystyle f'(3)$ where $\displaystyle f(x)=\frac{1}{2x-5}$

Pretty sure limit here is zero, but I do not understand how I would visualize this with much harder equations...

2. $\displaystyle f'(2)$ where $\displaystyle f(x)=x^3$

3. $\displaystyle f'(4)$ where $\displaystyle f(x)=\sqrt{2x-1}$

Also confused about questions asking to compute limits that involve infinity:

1. $\displaystyle \lim_{x \to \infty}\frac{1}{x^2}$

2. $\displaystyle \lim_{x \to \infty}\frac{5x+3}{3x-2}$

3. $\displaystyle \lim_{x \to \infty}\frac{x^2+x}{x^2-1}$

Read the textbook a few times but cannot seem to grasp it... Would appreciate some help or at least a guide that is easy to comprehend.

Another concern is the +'s and -'s atop of infinity. As far as I understand, these signify which direction to count the limit from. Anymore help would be greatly appreciated!