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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to \infty } (\sqrt {{x^2} + 1} - x)$ is equal to
  • A
    $1$
  • B
    $-1$
  • ✓
    $0$
  • D
    None of these
✓

Answer

Correct option: C.
$0$
c
(c) On rationalising, we get

$\mathop {\lim }\limits_{x \to \infty } \,\frac{{{x^2} + 1 - {x^2}}}{{\sqrt {{x^2} + 1} + x}} = \mathop {\lim }\limits_{x \to \infty } \,\frac{1}{{\sqrt {{x^2} + 1} + x}} = 0.$

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