Answer
1
Work Step by Step
$\lim\limits_{t \to 0}\frac{\sqrt {1+t}-\sqrt {1-t}}{t}=\lim\limits_{t \to 0}\frac{\sqrt {1+t}-\sqrt {1-t}}{t}*\frac{\sqrt {1+t}+\sqrt {1-t}}{\sqrt {1+t}+\sqrt {1-t}}=\lim\limits_{t \to 0}\frac{1+t-(1-t)}{t(\sqrt {1+t}+\sqrt {1-t})}=\lim\limits_{t \to 0}\frac{2t}{t(\sqrt {1+t}+\sqrt {1-t})}=\lim\limits_{t \to 0}\frac{2}{\sqrt {1+t}+\sqrt {1-t}}=\frac{2}{\sqrt {1+(0)}+\sqrt {1-(0)}}=\frac{2}{2}=1$
