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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim \left(\frac{a^x-b^x}{x}\right)=$
  • A
    $\log \left(\frac{ b }{ a }\right)$
  • ✓
    $\log \left(\frac{a}{b}\right)$
  • C
    $\frac{a}{b}$
  • D
    $\log _{a^b}$
✓

Answer

Correct option: B.
$\log \left(\frac{a}{b}\right)$
(B)
$\lim _{x \rightarrow 0} \frac{ a ^x- b ^x}{x}=\lim _{x \rightarrow 0}\left(\frac{ a ^x-1}{x}\right)-\lim _{x \rightarrow 0}\left(\frac{b^x-1}{x}\right)$
$=\log a -\log b$
$=\log \left(\frac{ a }{ b }\right)$

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