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Question

The value of limn1n{sec2π4n+sec22π4n+.....sec2nπ4n} is

A
logc2
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B
π2
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C
4π
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D
e
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Solution

The correct option is C 4π
bacf(x)dx=limnni=1cf(xi)Δx
Or, bacf(x)dx=climnni=1f(xi)Δx

Thus Or, bacf(x)dx=cbaf(x)dx

As can be seen above limit of sum tending to infinity can be defined in terms of definite integration
Similarly we can write above equation of limit as definite integral as :
10sec2πx4dx(tanπx4π4)10=4π
Therefore Answer is C

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