Limits & Continuity: Let f(x)=begincases(x-1)^(1)/(2-x), & x>1,\ xneq2\\ k, & x=2endcases… | JEE Main 2018 | Yukti Vault

Yukti Vault

JEE Main 2018 (Online) 15th April Evening ShiftQuestion 1

Let $f(x)=\begin{cases}(x-1)^{\frac{1}{2-x}}, & x>1,\ x\neq2\\ k, & x=2\end{cases}$ The value of $k$ for which $f$ is continuous at $x=2$ is

Limits & Continuity

$e^{-2}$$e$$e^{-1}$✓ Correct answer$1$

Solution

Type $1^\infty$: $\lim_{x\to2}\frac{x-2}{2-x}=-1$, so $f\to e^{-1}$ and $k=e^{-1}$.

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