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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
Question
Evaluate the following limits:
$\lim _{x \rightarrow 2}\left[\frac{\log x-\log 2}{x-2}\right]$
✓

Answer

$\lim _{x \rightarrow 2} \frac{\log x-\log 2}{x-2}$
Put $x-2=\mathrm{h}$
$\therefore \quad x=2+\mathrm{h}$
Required limit
$ =\lim _{h \rightarrow 0} \frac{\log (2+h)-\log 2}{h}$
$=\lim _{h \rightarrow 0} \frac{\log \left(\frac{2+h}{2}\right)}{h}$
$=\lim _{h \rightarrow 0} \frac{\log \left(1+\frac{h}{2}\right)}{\frac{h}{2} \times 2}$
$=1 \times \frac{1}{2}$
$=\frac{1}{2} $

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