## hpfan101 one year ago How to find the limit of a funciton with radicals?

1. hpfan101

$\lim_{x \rightarrow 0} \left( \frac{ \sqrt{1+x}-\sqrt{1-x} }{ x } \right)$

2. hpfan101

$\left( \frac{ \sqrt{1+x}-\sqrt{1-x} }{ x } \right) \times \left( \frac{ \sqrt{1+x} +\sqrt{1-x}}{ \sqrt{1+x}+\sqrt{1-x} } \right)$

3. hpfan101

After multiplying by the conjugate, this is what I got: $\left( \frac{ {(1+x)}-{(1-x)} }{ (x)(\sqrt{1+x}+\sqrt{1-x}) } \right)$

4. hpfan101

Not sure what to do about the denominator but the numerator would simplify to just 2x.

5. anonymous

leave the denominator in factored for cancel the x top and bottom, then plug in 0

6. anonymous

nice $$\LaTeX$$ btw !!

7. hpfan101

@satallite73: Thanks!