Question

Defined $f:[-\frac{1}{2},\infty )\to R$ by $f\left(x\right)=\sqrt{1+2x},x\in [-\frac{1}{2},\infty )$. Then compute $\underset{x\to \left(\frac{1}{2}\right)}{lim}f\left(x\right).$ and also find $\underset{x\to \frac{-1}{2}}{lim}f\left(x\right)$

Answer 1

$f\left(x\right)=\sqrt{1+2x}$

${lim}_{x\to \frac{1}{2}}f\left(x\right)=\sqrt{1+2\left(\frac{1}{2}\right)}=\sqrt{2}$

${lim}_{x\to \frac{-1}{2}}f\left(x\right)=\sqrt{1+2(0-\frac{1}{2})}=0$