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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow a} \frac{x^{-5}-a^{-5}}{x^{-3}-a^{-3}}=$
  • A
    $\frac{9}{4 a^2}$
  • B
    $-\frac{5}{3 a^2}$
  • ✓
    $\frac{5}{3 a^2}$
  • D
    $-\frac{9}{4 a^2}$
✓

Answer

Correct option: C.
$\frac{5}{3 a^2}$
(C)
$\lim _{x \rightarrow a} \frac{x^m-a^m}{x^n-a^n}=\frac{m}{n} a^{m-n}$
$\lim _{x \rightarrow a} \frac{x^{-5}-a^{-5}}{x^{-3}-a^{-3}}=\frac{-5}{-3}$(a) ${ }^{-5-(-3)}=\frac{5}{3}$$(a)^{-2}=\frac{5}{3 a^2}$

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