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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to \infty} \frac{{2{x^2} + 3x + 4}}{{3{x^2} + 3x + 4}} $  is equal to
  • ✓
    $\frac{2}{3}$
  • B
    $1$
  • C
    $0$
  • D
    $\infty $
✓

Answer

Correct option: A.
$\frac{2}{3}$
a
(a) $\mathop {\lim }\limits_{x \to \,\infty } \,\,\frac{{2{x^2} + 3x + 4}}{{3{x^2} + 3x + 4}} = \mathop {\lim }\limits_{x \to \infty } \,\,\frac{{2 + \frac{3}{x} + \frac{4}{{{x^2}}}}}{{3 + \frac{3}{x} + \frac{4}{{{x^2}}}}} = \frac{2}{3}$.

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