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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{n \to \infty } {\left( {\frac{n}{{n + y}}} \right)^n}$ equals
  • A
    $0$
  • B
    $1$
  • C
    $1/y$
  • ✓
    ${e^{ - y}}$
✓

Answer

Correct option: D.
${e^{ - y}}$
d
(d) $\mathop {\lim }\limits_{n \to \infty } \,{\left( {\frac{n}{{n + y}}} \right)^n} = \mathop {\lim }\limits_{n \to \infty } \,{\left( {\frac{1}{{1 + \frac{y}{n}}}} \right)^n}$

$ = \mathop {\lim }\limits_{n \to \infty } \,{\left( {1 + \frac{y}{n}} \right)^{ - n}}$

$ = \mathop {\lim }\limits_{n \to \infty } \,{\left[ {{{\left( {1 + \frac{y}{n}} \right)}^n}} \right]^{ - 1}} = {e^{ - y}}$.

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