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If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x...

If `f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),( 2 cos pix + tan ^(-1)x ,,, 1 lt x le 2):}` is differentiable in `[0,2]` then: ([.] denotes greatest integer function)

A

`a = (1)/(6), b = (pi)/(4) - (13)/(6)`

B

`a =-(1)/(6), b = (pi)/(4)`

C

`a=-(1)/(6), b = (pi)/(4) - (13)/(6)`

D

None of these

Text Solution

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The correct Answer is:
A
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

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  7. "If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le ...

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  16. The left hand derivative of f(x)=[x]sin(pix) at x = k, k is an intege...

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  17. Which of the following functions is differentiable at x = 0? cos (|x|...

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  19. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

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  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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