Question

Evaluate the limit.

lim x--->0 sqrt(7-x) - sqrt(7+x)/x

I got 0 for the limit and my textbook says its wrong.

Answer 1

multiply by the conjugate

Answer 2

i did and i got - x/ 2sqrt(7)

Answer 3

you forgot you had an \(x\) in the denominator

Answer 4

yeah, but i canceled the -2x in the numerator by the x in the denominator...

Answer 5

when you cancel and \(x\) with a\(-2x\) you are left with \(-2\) not \(-x\)

Answer 6

do i multiply the numerator and denominator by sqrt(7-x) + sqrt(7+x)/sqrt(7-x) + sqrt(7+x)?

Answer 7

my textbook says the limit is -1/sqrt(7). So i am not sure what i did wrong :/

Answer 8

oh, nvm, i think i see my problem :)

Answer 9

actually, im still confused

Answer 10

should get
\[\frac{-2}{\sqrt{7-x}+\sqrt{7+x}}\] then put \(x=0\)

Answer 11

ah, i see now. the 2 cancels out

Answer 12

you get
\[\frac{-2}{\sqrt{7}+\sqrt{7}}=\frac{-1}{\sqrt7}\]

Answer 13

yes, lot of cancelling here

Answer 14

ok, thanks for your help :)

Answer 15

yw