1. ## Derivative Quiz Tomorrow

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

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

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

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

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

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

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

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!

2. ## Hope this helps

Hi VX-1

Finding solutions to the derivatives 2 and 3 isn't difficult but if you're being asked to solve them using limits thats a different story, the thing I used to do when solvin limits was substitute x - infinity with x = a very large number;

For example 1.

if we think of x being a very large number say 100000, then substitute it and solve it the answer is 1x10^-10 or effectively zero, we can say as x tends to infinity the limit is zero. (even though it is impossible to really divide by infinity)

For question 2 we have a very large number divided by a very large number, adding 3 or subtracting 2 would have a negligible effect, the answer is close enough to 1 that we can say the limit is one.

Hope that helped, good luck for your quiz