Question

lim (x^2-1)/(sqrt(x)-1)
x->1

Answer 1

using L'Hospital rule, lim x->a ( fx/gx) = lim x-> a (f'x/g'x)
so lim x->1 (x^2-1)/(sqrt(x)-1) = lim x->1 (2x)/ (1/2 x^-1/2)
= 2/ 1/2 = 4

Answer 2

but the ans in the book says 2

Answer 3

I have not learned L'hospital's rule yet

Answer 4

i'm pretty sure the answer is 4
if i use another way, by multiply it with sqrt(x)+1/sqrt(x)+1, i got the same anwer
lim x-> 1 (x-1)(x+1) (sqrt(x)+1)/(sqrt(x)-1)(sqrt(x)+1) =
lim x->1 (x-1)(x+1)(sqrt(x)+1)/(x-1) =
lim x->1 (x+1)(sqrt(x) +1) = 2(1+1) = 4

Answer 5

ok thank you very much!

Answer 6

you're welcome

Answer 7

f(x) = x^2 -1
---------
g(x) = sqrt(x) - 1

L'Hopital says that the limit of this function can be lim| f'/g'

2x
--------- = 4x sqrt(x) = 4(1)(sqrt(1)) = 4
1/2sqrt(x)

I agree ...... or messed it up :)