Q231 / 270 · NDA 2016 (Phase 1) · Mathematics

If $\lim _{x \rightarrow 0} \phi(x)=a^2$, where $a \neq 0$, then what is $\lim _{x \rightarrow 0} \phi\left(\frac{x}{a}\right)$ equal to?

  • Correct answer
    A
    $\mathrm{a}^2$
  • B
    $a^{-2}$
  • C
    $-\mathrm{a}^2$
  • D
    $-\mathrm{a}$

Solution

$\begin{aligned} & \lim _{x \rightarrow 0} \phi(x)=a^2 \quad a \neq 0 \\ & \Rightarrow \lim _{x \rightarrow 0} \phi\left(\frac{x}{a}\right)=a^2\end{aligned}$ [because function value is constant]

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

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