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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
If $f(x)$ be a function satisfying the condition that $f(x) = \frac{1}{3}\left[ {f(x + 6) + \frac{6}{{f(x + 7)}}} \right]$ and $f(x) \geq  0$ for all $x \in R$ .If $\mathop {\lim }\limits_{x \to \infty } f(x) = \sqrt m $ then value of $m$ is
  • ✓
    $3$
  • B
    $4$
  • C
    $6$
  • D
    $5$
✓

Answer

Correct option: A.
$3$
a
$f(x)=\frac{f(x+6)}{3}=\frac{2}{f(x+7)}$

$\mathop {\lim }\limits_{x \to \infty } f(x) = \sqrt m  = \frac{{\sqrt {3m} }}{3} + \frac{2}{{\sqrt 3 }}$

$m = \frac{m}{3} + 2$

So, $m = 3$

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