Question

hey guys can you please help me with this limit

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

use l'hopital's rule

Answer 5

or something.

Answer 6

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

Answer 7

it is 1/2... sorry.

Answer 8

how did u find it?

Answer 9

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

Answer 10

in the limit of x,y->0.

Answer 11

is this clear?

Answer 12

not really im confused...

Answer 13

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.

Answer 14

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

Answer 15

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.

Answer 16

thanks alot:)

Answer 17

sure.