OpenStudy (dls):

Limits again :|

6 years ago
OpenStudy (dls):

WAIT

6 years ago
OpenStudy (anonymous):

...

6 years ago
OpenStudy (dls):

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

6 years ago
hartnn (hartnn):

did u try multiply by conjugates ?

6 years ago
OpenStudy (dls):

yes but denominator is too big and messy

6 years ago
OpenStudy (anonymous):

trying it...

6 years ago
hartnn (hartnn):

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

6 years ago
OpenStudy (dls):

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

6 years ago
OpenStudy (anonymous):

seems to work

6 years ago
OpenStudy (dls):

how did u solve the den?

6 years ago
OpenStudy (anonymous):

-2/3? checking...

6 years ago
OpenStudy (dls):

yes correct

6 years ago
OpenStudy (anonymous):

multiply by the conjugates

6 years ago
OpenStudy (dls):

denominator..how to solve >.>

6 years ago
OpenStudy (dls):

seperate conjugates?

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (dls):

yes

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (dls):

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

6 years ago
OpenStudy (anonymous):

naw multiply by the conjugates of both numerator and denom.

6 years ago
OpenStudy (dls):

??

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (dls):

okay o.O

6 years ago
OpenStudy (dls):

what am i made to do!!

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (anonymous):

x is a factor in numerator as well...

6 years ago
OpenStudy (dls):

can't follow..

6 years ago
OpenStudy (anonymous):

ok?

6 years ago
OpenStudy (dls):

use drawing/equation

6 years ago
OpenStudy (anonymous):

{ 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) }

6 years ago
OpenStudy (anonymous):

ok?

6 years ago
OpenStudy (dls):

yes I did this

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (dls):

yes it is!

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (anonymous):

factor out an x in both

6 years ago
OpenStudy (dls):

yes it is

6 years ago
OpenStudy (dls):

okay

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (dls):

yes!

6 years ago
OpenStudy (anonymous):

ok?

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (dls):

yesyes!

6 years ago
OpenStudy (dls):

imhere only isit done?

6 years ago
OpenStudy (anonymous):

subs in x=0

6 years ago
OpenStudy (dls):

numerator turns out 0

6 years ago
OpenStudy (anonymous):

no.

6 years ago
OpenStudy (dls):

2(0)-1(0)

6 years ago
OpenStudy (dls):

wait what its + okay

6 years ago
OpenStudy (dls):

-1/3?

6 years ago
OpenStudy (dls):

isnt the denom 6? 3(2):?

6 years ago
OpenStudy (anonymous):

numerator is -4 denom is 6

6 years ago
OpenStudy (anonymous):

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

6 years ago