Functions Question 61
Question: $ \underset{x\to 0}{\mathop{\lim }},( \frac{a^{x}-b^{x}}{x} )= $
[EAMCET 1988; RPET 1995]
Options:
A) $ \log ( \frac{b}{a} ) $
B) $ \log ( \frac{a}{b} ) $
C) $ \frac{a}{b} $
D) $ \log a^{b} $
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Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{a^{x}-b^{x}}{x}=\underset{x\to 0}{\mathop{\lim }}( \frac{a^{x}-1}{x} )-\underset{x\to 0}{\mathop{\lim }}( \frac{b^{x}-1}{x} ) $ $ =\log a-\log b=\log ,(a/b) $ .
BETA
