Q73 / 120 · VITEEE 2016 · Mathematics

If $\mathrm{f}(\mathrm{x})=(1+\mathrm{x})^{2 / \mathrm{x}}$ for $\mathrm{x} \neq 0$ and $\mathrm{f}(0)=\mathrm{e}^{2}$ is

  • A
    left continuous only at $x=0$
  • B
    right continuous only at $x=0$
  • Correct answer
    C
    continuous at $x=0$
  • D
    discontinuous at $x=0$

Solution

$\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0}\left[(1+x)^{1 / x}\right]^{2}=e^{2}=f(0)$

Hence, the correct answer is option: 'C'.

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