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In order that the function $f(x)=(x+1)^{1 / x}$ is continuous at $x=0, f(0)$ must be defined as
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The correct answer is:
$f(0)=0$
Here $\lim _{x \rightarrow 0^+} f(x)=k, \lim _{x \rightarrow 0^-} f(x)=-k$ and $f(0)=k$
But $f(x)$ is continuous at $x=0$, therefore $k$ must be zero.
But $f(x)$ is continuous at $x=0$, therefore $k$ must be zero.
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