1. ## Limit problem

Use algebra to evaluate the limit exactly.

lim(h->0) (1/(a+h) - 1/a)/h

2. Originally Posted by bluejewballs
Use algebra to evaluate the limit exactly.

lim(h->0) (1/(a+h) - 1/a)/h
I saw you there, Jhevon. Beat you on this one . I'm gonna go back and edit now

And here's the edit:

Get a common denominator:

$\displaystyle \frac{1}{a+h} - \frac{1}{a} = \frac{a}{a(a + h)} - \frac{a+h}{(a+h)a}$

Simplify:

$\displaystyle = \frac{a - (a + h)}{a(a + h)} = \frac{-h}{a(a + h)}$.

Therefore:

$\displaystyle \frac{\frac{1}{a+h} - \frac{1}{a}}{h} = \frac{-1}{a(a + h)}$.

The limit should now be obvious.

3. thanks i kept getting 1/a^2 and i was told that was wrong.

4. Originally Posted by bluejewballs
thanks i kept getting 1/a^2 and i was told that was wrong.
that is wrong. it is -1/a^2

if you have any acquaintance with calculus, you'll realize this limit gives the derivative (by its definition) of 1/a with respect to a

5. Originally Posted by bluejewballs
thanks i kept getting 1/a^2 and i was told that was wrong.
So you see why the correct numerator is -1 ...?

6. Originally Posted by Jhevon
that is wrong. it is -1/a^2

if you have any acquintance with calculus, you'll realize this limit gives the derivative of 1/a with respect to a
beat me by 5 seconds .....payback time, hey?

7. Originally Posted by mr fantastic
beat me by 5 seconds .....payback time, hey?
exactly!

8. yeah i understand that it is -1 i just made a stupid mistake like i always do