Question

lim 1-sqrtx/1-x as x goes to 1

Answer 1

factor 1-x :)

Answer 2

or

Answer 3

IF you don't like that rationalize the numerator

Answer 4

I prefer the first way :)

Answer 5

\[a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})\]

Answer 6

could explain it to me I think I got stuck after that part.

Answer 7

Did you factor 1-x?
What did you get?

Answer 8

is it 1/x I'm not sure

Answer 9

Ok since you can't factor 1-x using the formula I gave
Then do you know how to rationalize the numerator?

Answer 10

yes

Answer 11

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

Answer 12

Now solve..:)

Answer 13

like for example pretend I wanted to factor
9-x
using the formula I gave it would be
\[(3-\sqrt{x})(3+\sqrt{x})\]

Answer 14

But you can always go the rationalizing the numerator way for this one
Just multiply both top and bottom by top's conjugate

Answer 15

so on top would be \[(1+\sqrt{x})(\sqrt{x-1})\] right?

Answer 16

No your second factor is a bit messed up

Answer 17

or would it be x-1

Answer 18

\[4-x=(2-\sqrt{x})(2+\sqrt{x})\]
\[9-x=(3-\sqrt{x})(3+\sqrt{x})\]
\[16-x=(4-\sqrt{x})(4+\sqrt{x})\]
\[25-x=(5-\sqrt{x})(5+\sqrt{x})\]
Do you see I'm just using the formula above:
\[a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})\]

Answer 19

So
\[1-x=(1-\sqrt{x})(1+\sqrt{x})\]

Answer 20

Got it?

Answer 21

yes

Answer 22

so that would be on top and bottom Right?

Answer 23

ok where you have 1-x you will have
\[(1-\sqrt{x})(1+\sqrt{x})\]

Answer 24

which is on bottom right?

Answer 25

yes

Answer 26

Ok so does anything cancel?

Answer 27

yes the \[1-\sqrt{x}\] which 1 is on the bottom and top right?

Answer 28

\[\lim_{x \rightarrow 1}\frac{1-\sqrt{x}}{1-x}=\lim_{x \rightarrow 1}\frac{1-\sqrt{x}}{(1-\sqrt{x})(1+\sqrt{x})}\]
You have the factor \[1-\sqrt{x}\]
on both top and bottom so cancel it

Answer 29

ok so all I will have left is 1+sqrt x on bottom which is 1+the sqrt of 1 =2 Right? so the anserw is 1/2

Answer 30

that's right

Answer 31

thanks myininaya