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OpenStudy (lalaly):

hey guys can you please help me with this limit

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OpenStudy (lalaly):

\[\lim_{x,y \rightarrow 0,0}(\sqrt{1+x ^{2}} - \sqrt{1+y ^{2}}) / x ^{2}-y ^{2}\]

OpenStudy (anonymous):

is there a bracket (x^2-y^2)?

OpenStudy (anonymous):

it does matter. if so, it is 1/(x+y).

OpenStudy (anonymous):

use l'hopital's rule

OpenStudy (anonymous):

or something.

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OpenStudy (lalaly):

i tried....it didnt work,,,,can u plz show me how

OpenStudy (anonymous):

it is 1/2... sorry.

OpenStudy (lalaly):

how did u find it?

OpenStudy (anonymous):

\[\sqrt{1+x ^{2}}=1+x ^{2}/2 .\sqrt{1+y ^{2}}=1+y^{2}/2\]

OpenStudy (anonymous):

in the limit of x,y->0.

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OpenStudy (anonymous):

is this clear?

OpenStudy (lalaly):

not really im confused...

OpenStudy (anonymous):

so, the numerator becomes: (1+x^2/2) - (1+y^2/2) = (x^2-y^2)/2. the denominator is x^2-y^2. so the answer is 1/2.

OpenStudy (lalaly):

ohh okkk....i got it....Thanks

OpenStudy (anonymous):

in the limit of x->0, (1+x)^a -> 1+ax. in this case, x is actually x^2. a = 1/2. so (1+x^2)^(1/2) -> 1+(x^2)/2.

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OpenStudy (lalaly):

thanks alot:)

OpenStudy (anonymous):

sure.

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