Question

How to do this?
As the limit of x approaches 0 ((1/Sqt 1+s) -1) / s

Answer 1

do you know how to rationalize ?

Answer 2

by multiplying with the conjugate ?

Answer 3

yes

Answer 4

but nothing cancels out you still have 0/0

Answer 5

ok,
so, first step was to cross-multiply in numerator

1/sqrt(s+1) -1 = (1-sqrt(s+1)) / sqrt(s+1)

got this ?

Answer 6

why do you cross multiply..?

Answer 7

just a simplification technique....i mean, what else we can do :P

Answer 8

now we rationalize the numerator!
by multiplying and dividing by
1+sqrt(s+1)

Answer 9

yes i got that

Answer 10

good, so what does numerator simplify to ?

Answer 11

you get 1(sqt 1-s) - 1+s ...right?

Answer 12

the numerator now has \((1-\sqrt{s+1})(1+\sqrt{(s+1)})\)
right ?

Answer 13

yes

Answer 14

and the denominater is (1-s)s right?

Answer 15

the denominator will be \(s \sqrt{s+1}(1+\sqrt{s+1})\)
didn't u get this ?

Answer 16

in the numerator, you use
(a+b)(a-b)= a^2-b^2

Answer 17

hmm I'm lost

Answer 18

focus on numerator first ?

Answer 19

Just ot be sure that is what you started out with right? as the equation
\[(1\div \sqrt{1+s}) - 1 \div s\]

Answer 20

sorry, i got to go
the numerator becomes
1- (s+1)
= -s

this 's' gets cancelled with denominator's 's'
and then if you plug in s=0, you will not get 0/0 form.
good luck :)

Answer 21

yes, thats what i started with...

Answer 22

=
(1-sqrt (s+1)-1)/ [s sqrt(s+1)]

will be next step

Answer 23

hold up I think i got it, what did you end up with your final answer?

Answer 24

limit is -1/2

Answer 25

err I got 0

Answer 26

well following @hartnn steps you should end up with:
\[\frac{-s}{s \sqrt{1+s}(1+\sqrt{1+s})}\]
the "s" cancels
plug in s=0