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Question: Answered & Verified by Expert
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?
MathematicsLimitsNDANDA 2016 (Phase 1)
Options:
  • A $\mathrm{a}^{2}$
  • B $\mathrm{a}^{-2}$
  • C $-\mathrm{a}^{2}$
  • D -a
Solution:
2193 Upvotes Verified Answer
The correct answer is: $\mathrm{a}^{2}$
$\begin{aligned} & \lim _{x \rightarrow 0} \phi(x)=a^{2} \\ & \Rightarrow \lim _{x \rightarrow 0} \phi\left(\frac{x}{a}\right)=a^{2} \end{aligned}$
$a \neq 0$
[because function value is constant]

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