If the function $f(x)=\frac{\sqrt{1+x}-1}{x}$ is continuous at $x=0$ then $f(0)=$

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { } \lim _{x ightarrow 0} f(x)=f(0) \Rightarrow f(0)=\lim _{x ightarrow 0} \frac{\sqrt{1+x}-1}{x} \ & =\lim _{x ightarrow 0} \frac{1+x-1}{x(\sqrt{1+x}+1)}=\lim _{x ightarrow 0} \frac{1}{1+\sqrt{1+x}}=\frac{1}{2}\end{aligned}$

If the function $f(x)=\frac{\sqrt{1+x}-1}{x}$ is continuous at $x=0$ then $f(0)=$

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