Help Notes: What is the limit x-->0 (sqrt(1+x)-sqrt(1-x))/x ?

Monday, 31 October 2011

What is the limit x-->0 (sqrt(1+x)-sqrt(1-x))/x ?

You should
substitute 0 for x such that:

$\displaystyle\lim_{{{x}\to{0}}}\frac{{\sqrt{{{1}+{x}}}-\sqrt{{{1}-{x}}}}}{{x}}=$
(sqrt(1+0) - sqrt(1-0))/0

$\displaystyle\lim_{{{x}\to{0}}}\frac{{\sqrt{{{1}+{x}}}-\sqrt{{{1}-{x}}}}}{{x}}=\frac{{{1}-{1}}}{{0}}$
= 0/0

The indetermination 0/0 could be solved using l'Hospital's
theorem...

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