Applications Of Derivatives Question 276
Question: For all $ x\in (0,,1) $
[IIT Screening 2000]
Options:
A) $ e^{x}<1+x $
B) $ {\log_{e}}(1+x)<x $
C) $ \sin x>x $
D) $ {\log_{e}}x>x $
Show Answer
Answer:
Correct Answer: B
Solution:
Both $ e^{x} $ and $ 1+x $ are increasing and $ \sqrt{e}\ge 1+\frac{1}{2}, $ because $ \sqrt{e}=1.65 $ nearly. so the answer is not correct.
Since $ \sin \frac{\pi }{6}<\frac{\pi }{6} $ because $ \frac{1}{2}<\frac{22}{42} $ . So, is not correct.
$ \log \frac{1}{2}<\frac{1}{2} $ because $ \log \frac{1}{2} $ is negative.
$ \therefore $ Option is not correct.
Thus, by elimination is correct.
BETA
