Functions Question 189
Question: $ \underset{x\to 0}{\mathop{\lim }},[ \frac{\sin (x+a)+\sin (a-x)-2\sin a}{x\sin x} ]= $
Options:
A) $ \sin a $
B) $ \cos a $
C) $ -\sin a $
D) $ \frac{1}{2}\cos a $
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Answer:
Correct Answer: C
Solution:
$ \underset{x\to 0}{\mathop{\lim }},2,\sin ,a,.,\frac{(\cos x-1)}{x\sin x} $ $ =-2,\sin a,.,\frac{(1-\cos x)}{x^{2}},.,( \frac{x}{\sin x} ) $ $ =\underset{x\to 0}{\mathop{\lim }},-2\sin a,.,\frac{2,{{\sin }^{2}}(x/2)}{4,{{( \frac{x}{2} )}^{2}},( \frac{\sin x}{x} )}=-\sin a $ .
BETA
