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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Mathematics
Chapter
Limits

BITSAT 2016 · Mathematics · Limits

_ n arrow ∞ a^ n +b^ n a^ n -b^ n , where a > b > 1, is equal to

lim⁡n→∞an+bnan−bn,\lim _{n \rightarrow \infty} \frac{a^{n}+b^{n}}{a^{n}-b^{n}}, where a>b>1,a > b > 1, is equal to

Options

  1. A-1
  2. B1
  3. C0
  4. DNone

Correct answer

B. 1

Step-by-step solution

limit =\lim _{n \rightarrow \infty} \frac{1+\left(\frac{b}{a}\right)^{n}}{1-\left(\frac{b}{a}\right)^{n}}=1,becausebecause0\lt \frac{b}{a}\lt 1impliesimplies\left(\frac{b}{a}\right)^{n} \rightarrow 0asasn \rightarrow \infty
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