A) \[{{\alpha }_{n}}<{{\beta }_{n}}<\frac{\pi }{4}\]
B) \[{{\alpha }_{n}}>{{\beta }_{n}}>\frac{\pi }{4}\]
C) \[{{\alpha }_{n}}>\frac{\pi }{4}>{{\beta }_{n}}\]
D) \[{{\alpha }_{n}}<\frac{\pi }{4}<{{\beta }_{n}}\]
Correct Answer: D
Solution :
[d] \[f(x)=\frac{1}{1+{{x}^{2}}}\] is decreasing function Clearly, \[{{\alpha }_{n}}\] represents the area of n rectangles below the graph of \[\frac{1}{1+{{x}^{2}}}\]as shown in the following diagram:You need to login to perform this action.
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