Posted by
**ronan** on
.

l = lim as x approaches 0 of x/(the square root of (1+x) - the square root of (1-x)

decide whether:

l=-1

or

l=0

or

l=1

Let me make sure I understand the question. Do we have

lim x->0 x/[sqrt(1+x) - sqrt(1-x)] ?

If so then multiply the expression by

[sqrt(1+x) + sqrt(1-x)]/[sqrt(1+x) + sqrt(1-x)]

to get

(x*[sqrt(1+x) + sqrt(1-x)])/[(1+x) - (1-x)]=

(x*[sqrt(1+x) + sqrt(1-x)])/2x=

=limx->0 [sqrt(1+x) + sqrt(1-x)]/2=

something you can do.

biz