Question

Confirm the limit algebraically:

lim ((1/2+x)-.5)/x
x->0

Answer 1

The limit is 2 but Im not sure how to confirm it.

Answer 2

use L'Hopital's rule

Answer 3

((1/(2+x))-.5)/x - Extra parentheses

Answer 4

Looking that up right now, thanks.

Answer 5

\[\frac{ \frac{ 1 }{ 2+x }-5 }{ x }?\]

Answer 6

yes that's right, sorry it wasn't clear.

Answer 7

Oh, theres no 5. Its 1/2.

Answer 8

i c

Answer 9

wait what's 1/2?

Answer 10

The limit zzr0ck3r made. Instead of -5 its -.5

Answer 11

Rewrite that as:
(1/(2+x))/x - (1/2/x)

Answer 12

wait I don't see how that helps

Answer 13

Just looked up a L'Hopital video by Khan. I think I get it now.

Answer 14

L'Hopital's rule is the easiest way for these types of limits, seriously

Answer 15

\[\lim_{x \rightarrow 0}\frac{\frac{1}{2+x}-\frac{1}{2}}{x}\]
\[\lim_{x \rightarrow 0}\frac{\frac{2}{2*(2+x)}-\frac{(2+x)}{2*(2+x)}}{x}\]

Answer 16

before i continue i must stress
ALGEBRAICALLY

Answer 17

the answer is not 2

we have 2-(2+x)/(2*(2+x))/x

= -1/(4+2x) run limit = -1/4

Answer 18

Fudge sorry. That was the limit to another question I did.

Answer 19

(2-(2+x))/(2*(2+x))*1/x simplify

-1/(4+2x) run limit

-1/4

Answer 20

http://www.twiddla.com/929034

Answer 21

dont use lhopital if you dont know it

Answer 22

\[\lim_{x \rightarrow 0}\frac{\frac{2-2-x}{2*(2+x)}}{x}\]
\[\lim_{x \rightarrow 0}\frac{\frac{-x}{2*(2+x)}}{x}\]
\[\lim_{x \rightarrow 0}\frac{-1}{2*(2+x)}\]

Answer 23

oh you guys finished it here.. sorry didn't notice.

Answer 24

:) im to fast:P

Answer 25

pretty easy when you arnt using latex:P

Answer 26

zzr0ck3r - *le challenge accepted*

Answer 27

typing it out in latex is annoying but nice to look at

Answer 28

I already won the challenge.:P

Answer 29

Wow that's fantastic Agent. It looks like a great resource.
Thanks everyone for helping, Ill make sure I understand it.

Answer 30

yeah I agrea completeidiot even more so with this problem x/y/c/x:)

Answer 31

Wish I could best answer you all.

Answer 32

lol what ever

Answer 33

didnt I answer it twice before those slowpokes?

Answer 34

im jk I could not care less:P