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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 2} \frac{x^{100}-2^{100}}{x^{77}-2^{77}}$ is equal to
  • A
    $\frac{100}{77}$
  • B
    $\frac{100}{77}\left(2^{22}\right)$
  • C
    $\frac{100}{77}\left(2^{21}\right)$
  • ✓
    $\frac{100}{77}\left(2^{23}\right)$
✓

Answer

Correct option: D.
$\frac{100}{77}\left(2^{23}\right)$
(D)
$\lim _{x \rightarrow a} \frac{x^m-a^m}{x^n-a^n}=\frac{m}{n} a^{m-n}$
$\lim _{x>2} \frac{x^{100}-2^{100}}{x^{77}-2^{77}}=\frac{100}{77}$$(2)^{100-77}=\frac{100}{77}\left(2^{23}\right)$

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