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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Limits

NDA 2016 · Mathematics · Limits

If _ x arrow 0 φ(x)=a^2 , where a ≠ 0 , then what is _ x arrow 0 φ...

If lim⁡x→0ϕ(x)=a2\lim _{x \rightarrow 0} \phi(x)=a^2, where a≠0a \neq 0, then what is lim⁡x→0ϕ(xa)\lim _{x \rightarrow 0} \phi \left(\frac{x}{a}\right) equal to?

Options

  1. Aa2\mathrm{a}^2
  2. Ba−2a^{-2}
  3. C−a2-\mathrm{a}^2
  4. D−a-\mathrm{a}

Correct answer

A. a2\mathrm{a}^2

Step-by-step solution

lim⁡x→0ϕ(x)=a2a≠0⇒lim⁡x→0ϕ(xa)=a2\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]
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