Question

whats the limit of the following function? could somebody help me pleasE?

Answer 1

\[\frac{ \sqrt{2-t}-\sqrt{2} }{ t }\]

Answer 2

t-->0

Answer 3

first you want to multiply the top and bottom by the reciprocal of the top

Answer 4

\[\sqrt{2-t}+\sqrt{2}\]

Answer 5

multiply top and bottom by that, and what do you get?

Answer 6

yeep, but then i'll get this: \[\frac{ 2-t-2 }{ t(\sqrt{2-t})+\sqrt{2}}\]

Answer 7

right.

Answer 8

now simplify the top

Answer 9

ill get:\[\frac{ -t }{ t(\sqrt{2-t} +\sqrt{2}) }\]

Answer 10

also, the denominator should be \[t(\sqrt{2-t}+\sqrt{2})\]

Answer 11

correct. now can you do anything with the top and bottom t's?

Answer 12

is it right to cancel a negative t with a positive t ?

Answer 13

well, you just cancel the t's, the negative would stay.

Answer 14

so you would get \[\frac{ -1 }{ \sqrt{2-t}+\sqrt{2} }\]

Answer 15

now you can take the limit directly by plugging in 0.

Answer 16

:O so the limit is: -0.353509207 ?

Answer 17

well, I suppose if you want to do it that way, I would just say \[\frac{ -1 }{ 2\sqrt{2} }\]

Answer 18

oh God youre a genius! thank you so much!!!

Answer 19

:) no worries.