Question

Evaluate limit ((x/(1+(sqrtx))-(1/2))/(x-1)

Answer 1

as x approaches 1

Answer 2

1/2 maybe

http://www.wolframalpha.com/input/?i=limit {x+to+0}%28%28x%2F%281%2B%28sqrtx%29%29-%281%2F2%29%29%2F%28x-1%29

Answer 3

I have the answer, I just want to know where I'm going wrong in solving it.

Answer 4

well then :) ..... whatcha got written?

Answer 5

So far, I've only combined the numerator.

Answer 6

Then I get (2x-1-(sqrtx))/(2*(1+(sqrtx)))/(x-1)

Answer 7

Then I get lost

Answer 8

I set it up where you should multiply by the reciprocal

Answer 9

then took the radical outside of the denominator

Answer 10

now I'm stuck

Answer 11

\[\frac{\frac{x}{(1+\sqrt{x})}-\frac{1}{2}}{x-1}\] this the function?

Answer 12

yes

Answer 13

2x -1 - sqrt(x))
---------------- right?
2 (1+sqrt(x)) (x-1)

Answer 14

yes.

Answer 15

as x-> 1 we need to determine if the top can control it..... does it factor...

Answer 16

yes, it does.

Answer 17

what do we get for the top then?

Answer 18

let me do the quadratic I guess.

Answer 19

(\[(\sqrt{x}+1)(\sqrt{x}-1/2)\]

Answer 20

I don't think that's right though?

Answer 21

2a^2 -a -1 ; a=sqrt(x)

(a-2/2)(a+1/2)

a = 1, -1/2

sqrt(x) = 1, -1/2; i agree

Answer 22

oh yes it does. :)

Answer 23

(sqrt(x)-1) (2sqrt(x)+1)
--------------------
2 (sqrt(x)+1) (x-1)

we are closer i think lol

Answer 24

I still divide by zero.

Answer 25

gotta go over and make sure I aint missed nuthin

Answer 26

you cancel out the 2(sqrtx+1) on top and bottom.

Answer 27

2x - sqrt(x)) -1
----------------
2 (1+sqrt(x)) (x-1)


(sqrt.x -1)(2sqrt.x +1)
--------------------
(sqrt.x +1) (2x-2)


(sqrt.x -1)(2sqrt.x +1)
------------------------
2x sqrt(x) -2sqrt(x) +2x -2



(sqrt.x -1)(2sqrt.x +1)
------------------------
2(x sqrt(x) -sqrt(x) +x -1)

this is my thougths so far; the bottom factors by grouping maybe

Answer 28

eeek.

Answer 29

2[sqrt(x)(x-1) + 1(x-1)]

2 (sqrt(x)+1) (x-1)....

somehow this converts to:

2(sqrt(x)-1)(sqrt(x)+1)^2

Answer 30

http://www.wolframalpha.com/input/?i=%282%2B2sqrt%28x%29%29%28x-1%29

Answer 31

woah, ok.

Answer 32

http://www.wolframalpha.com/input/?i=lim {x+to+1}%28%28x%2F%281%2B%28sqrtx%29%29-%281%2F2%29%29%2F%28x-1%29

this shows steps...

Answer 33

i dont know why it cuts the link short in firefox.... but copy paste that into the address bar and you shouldbe able to see how they stepped thru it

Answer 34

Oh well, that's inconsistent with the answer key. But thanks for all your help. :)