Tuesday
April 21, 2015

Homework Help: math calculus please help!

Posted by ronan on Wednesday, September 27, 2006 at 8:27am.

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

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