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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
If $\mathop {\lim }\limits_{x \to 0} \phi (x) = {a^3},(a \ne 0)$; then $\mathop {\lim }\limits_{x \to 0} \phi \left( {\frac{x}{a}} \right)$ is equal  to :-
  • A
    $\frac{1}{a^3}$
  • ✓
    $a^3$
  • C
    $a^2$
  • D
    $\frac{1}{a^2}$
✓

Answer

Correct option: B.
$a^3$
b
$\lim _{x \rightarrow 0} \phi\left(\frac{x}{a}\right)=\lim _{a t \rightarrow 0}\left(\frac{a t}{a}\right)$

$=\lim _{t \rightarrow 0} \phi(t)=\lim _{x \rightarrow 0} \phi(x)=a^{3}$

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