Calculus: Limits: Simple question

[Ultima]

It's been a long time since I've touched Math, and now I'm taking a Calculus course.. can anyone refresh my memory on how I would solve the following expression?

.. 1 ........... 1
------ .. - .. ---
a + h ........ a
----------------
........h........

or (( 1 / a + h) - ( 1 / a)) / h

a != 0


The limit is h-> 0. I can figure it out once I simplify the expression, but I forget how to deal with the 1 / stuff....

Edit:

 

[Tu13erhead]

This is the limit as, h->0 or h-> infinity?

 

[Ultima]

Originally posted by: Tu13erhead
This is the limit as, h->0 or h-> infinity?

h->0

 

[Hanpan]

http://pics.bbzzdd.com/users/hanpan/calc2.JPG

 

[Hanpan]

any further questions just ask.

 

[Ultima]

Originally posted by: Hanpan
any further questions just ask.

Could you just tell me in more detail how you got from (1 / x + h) - ( 1 / x) to (x - x - h) / (x^2 + xh) ? Thx...

 

[chuckywang]

Originally posted by: Ultima

Originally posted by: Hanpan
any further questions just ask.

Could you just tell me in more detail how you got from (1 / x + h) - ( 1 / x) to (x - x - h) / (x^2 + xh) ? Thx...

1/(x+h)-1/x = x/(x*(x+h)) - (x+h)/(x*(x+h)) = (x-(x+h))/(x*(x+h)) = -h/(x*(x+h)).

 

[Hanpan]

Originally posted by: chuckywang

Originally posted by: Ultima

Originally posted by: Hanpan
any further questions just ask.

Could you just tell me in more detail how you got from (1 / x + h) - ( 1 / x) to (x - x - h) / (x^2 + xh) ? Thx...

1/(x+h)-1/x = x/(x*(x+h)) - (x+h)/(x*(x+h)) = (x-(x+h))/(x*(x+h)) = -h/(x*(x+h)).

That about covers it.

 

[hypn0tik]

Originally posted by: Ultima

Originally posted by: Hanpan
any further questions just ask.

Could you just tell me in more detail how you got from (1 / x + h) - ( 1 / x) to (x - x - h) / (x^2 + xh) ? Thx...

Basically he brought everything to a common denominator.

Just like 1/3 + 1/4 = (4 + 3)/12

 

[Ultima]

I'm trying to get it... but remember, I haven't even looked at algebra in more than a year...

What do I multiply the top half by to simplify it? I don't see how to get to your results.

 

[blueshoe]

Originally posted by: Ultima
I'm trying to get it... but remember, I haven't even looked at algebra in more than a year...

What do I multiply the top half by to simplify it? I don't see how to get to your results.

You multiply the first part of the top by x/x and multiply the second part by (x+h)/(x+h)

 

[Hanpan]

Put everything over a common denominator, factor out the h, and voila you're done.