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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{n \rightarrow \infty} \frac{3.2^{n-1}-4.5^{n-1}}{5.2^n+7.5^n}=$
  • ✓
    $\frac{-20}{7}$
  • B
    $0$
  • C
    $\frac{3}{5}$
  • D
    $\frac{-4}{7}$
✓

Answer

Correct option: A.
$\frac{-20}{7}$
(A)
$\lim _{ n \rightarrow \infty} \frac{3.2^{ n +1}-4.5^{ n +1}}{5.2^{ n }+7.5^{ n }}$
$=\lim _{n \rightarrow \infty} \frac{6.2^n-20.5^n}{5.2^n+7.5^n}=\lim _{n \rightarrow \infty} \frac{5^n\left[6(2 / 5)^n-20\right]}{5^n\left[5(2 / 5)^n+7\right]}$
$=-\frac{20}{7} \quad \ldots . .\left[\because n \rightarrow \infty,\left(\frac{2}{5}\right)^n \rightarrow 0\right]$

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