For a, b > 0, let - Vidyadip

MCQ

For $a, b > 0,$ let

A
5
B
4
C
8
D
6

✓

Answer

$\lim _{x \rightarrow 0} f(x)=f(0)=3$
$\lim _{x \rightarrow 0^{+}} \frac{\sqrt{a x+b^2 x^2}-\sqrt{a x}}{b \sqrt{a} x \sqrt{x}}=3$
$\lim _{x \rightarrow 0^{+}} \frac{a x+b^2 x^2-a x}{b \sqrt{a} x^{3 / 2}\left(\sqrt{a x+b^2 x^2}+\sqrt{a x}\right)}$
$\lim _{x \rightarrow 0^{+}} \frac{b^2}{b \sqrt{a}\left(\sqrt{a+b^2 x}+\sqrt{a}\right)}$
$\frac{b}{\sqrt{a} \cdot 2 \sqrt{a}} $
$\Rightarrow \frac{b}{2 a}=3 $
$\Rightarrow \frac{b}{a}=6$

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