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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{ a ^x- b ^x}{ e ^x-1}=$
  • ✓
    $\log \left(\frac{a}{b}\right)$
  • B
    $\log \left(\frac{ b }{ a }\right)$
  • C
    $\log (a b)$
  • D
    $\log (a+b)$
✓

Answer

Correct option: A.
$\log \left(\frac{a}{b}\right)$
(A)
Applying L-Hospital's rule, we get
$\lim _{x \rightarrow 0} \frac{a^x-b^x}{e^x-1}=\lim _{x \rightarrow 0} \frac{a^x \log a-b^x \log b}{e^x}$
$=\log a-\log b=\log \left(\frac{a}{b}\right)$

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