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Q.

Let f(x)=sinx2πx22x18+ax3+b     for  0x12cosπx+tan1x     for 1<x2 is differentiable in [0,2],[x] denotes the greatest integer less than or equal to x. then

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a

a=14

b

b=π4136

c

a=16

d

b=π4116

answer is A, D.

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Detailed Solution

f(x)=ax3+b    for 0x12cosπx+tan1x    for 1<x2

Since f(x) is continuous at x=1a+b=2+π4(1)

Also f(x) is differentiable at x=1a=16

From (1) 16+b=-2+π4 b=-2-16+π4 b=π4-136

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