Question

Limits again :|

Answer 1

WAIT

Answer 2

...

Answer 3

\[\lim_{x \rightarrow 0}\frac{{\sqrt{1+2x^2}}-{\sqrt{1+x}}}{\sqrt{4+4x^2}-\sqrt{4-3x}}\]

Answer 4

did u try multiply by conjugates ?

Answer 5

yes but denominator is too big and messy

Answer 6

trying it...

Answer 7

u get 4x^2 +3x in denom.
and 2x^2 - x in numerator

Answer 8

i got just the numerator,denominator is scary to solve!

Answer 9

seems to work

Answer 10

how did u solve the den?

Answer 11

-2/3?
checking...

Answer 12

yes correct

Answer 13

multiply by the conjugates

Answer 14

denominator..how to solve >.>

Answer 15

seperate conjugates?

Answer 16

denom is (4x-3){ sqrt(1+2x^2) +sqrt(1+x) }

Answer 17

yes

Answer 18

lim (4x-3){ sqrt(1+2x^2) +sqrt(1+x) } = -6
x->0

Answer 19

I have
(root of 4+4x^2 - root of 4-3x) (root o f 1+2x^2 + root of 1+x)

Answer 20

naw multiply by the conjugates of both numerator and denom.

Answer 21

??

Answer 22

so multiply that by sqrt(4+4x^2) +sqrt(4-3x) (also multiply it in the numerator though :P)

Answer 23

okay o.O

Answer 24

what am i made to do!!

Answer 25

(4x^2 -3x)*(root o f 1+2x^2 + root of 1+x)

Answer 26

=x*(4x -3)*(root o f 1+2x^2 + root of 1+x)

Answer 27

x is a factor in numerator as well...

Answer 28

can't follow..

Answer 29

ok?

Answer 30

use drawing/equation

Answer 31

{ sqrt(4+4x^2) +sqrt(4-3x) }{ sqrt(1+2x^2) +sqrt(1+x) }
------------------------------------------------------
{ sqrt(4+4x^2) +sqrt(4-3x) }{ sqrt(1+2x^2) +sqrt(1+x) }

Answer 32

ok?

Answer 33

yes I did this

Answer 34

great, then your numerator is
( 2x^2-x)(sqrt(4+4x^2) +sqrt(4-3x) }

Answer 35

yes it is!

Answer 36

denom is
(4x^2-3x){ sqrt(1+2x^2) +sqrt(1+x) }

Answer 37

factor out an x in both

Answer 38

yes it is

Answer 39

okay

Answer 40

x( 2x-1)(sqrt(4+4x^2) +sqrt(4-3x) }
x(4x-3){ sqrt(1+2x^2) +sqrt(1+x) }

Answer 41

yes!

Answer 42

ok?

Answer 43

that's it, hole is gone. subs in x=0

Answer 44

( 2x-1)(sqrt(4+4x^2) +sqrt(4-3x) }
-----------------------------------
(4x-3){ sqrt(1+2x^2) +sqrt(1+x) }

Answer 45

yesyes!

Answer 46

imhere only
isit done?

Answer 47

subs in x=0

Answer 48

numerator turns out 0

Answer 49

no.

Answer 50

2(0)-1(0)

Answer 51

wait what its +
okay

Answer 52

-1/3?

Answer 53

isnt the denom 6?
3(2):?

Answer 54

numerator is -4 denom is 6

Answer 55

I have sign wrong:
should be:
( 2x-1)(sqrt(4+4x^2) +sqrt(4-3x) }
-----------------------------------
(4x+3){ sqrt(1+2x^2) +sqrt(1+x) }