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Question

Let f be a continuous and differentiable function in (a,b), limxa+f(x) and limxbf(x). If f(x)+f2(x)1 for a<x<b, then

A
baπ
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B
baπ
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C
ba=π
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D
None of these
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Solution

The correct option is B baπ
We have f(x)+f2(x)1

f(x)1+f2(x)+10, for x(a,b) ...(1)

h(x)=tan1f(x)+x, is a non-decreasing function in the interval (a,b)

limxah(x)limxah(x)

limxa+(tan1f(x)+x)limxb(tan1f(x)+x)

π2+aπ2+b

Hence baπ

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