Advertisement Remove all ads

Lim X → 2 X − 2 Log a ( X − 1 ) - Mathematics

\[\lim_{x \to 2} \frac{x - 2}{\log_a \left( x - 1 \right)}\]

Advertisement Remove all ads

Solution

\[\lim_{x \to 2} \left[ \frac{x - 2}{\log_a \left( x - 1 \right)} \right]\]

Let x = 2 + h

 x → 2
∴ h → 0

\[= \lim_{h \to 0} \left[ \frac{\left( 2 + h \right) - 2}{\frac{\log \left\{ \left( 2 + h \right) - 1 \right\}}{\log a}} \right]\]
\[ = \log a \lim_{h \to 0} \left[ \frac{h}{\log \left( 1 + h \right)} \right]\]
\[ = \log a \times 1\]

 

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 10 | Page 71
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×