Let f: R R be defined by f(x)= array ccc + [x] x , & if & x0 2, & if & x=0 + [ x-x x^3 ], & if & x

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Let f: R R be defined by f(x)= array ccc + [x] x , & if & x>0 2, & if & x=0 + [ x-x x^3 ], & if & x < 0 array . where, [x] denotes the integral part of x . If f continuous at x=0 , then - is equal to

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Correct answer: B. 1

Given. f(x)= array lll + [x] x , & if & x>0 2, & if & x=0 + [ x-x x^3 ], & if & x < 0 array . Since, f is continuous at x=0 . IHI =f(0)= RHI. Now, I.HI. = f(x) aligned & = _ x 0 [ + ( x-x x^3 ) ] & = _ h 0 [ + ( h+h -h^3 ) ] & = +0 aligned RHL = _ x 0⁺ [ + [x] x ] aligned & = _ h 0 [ + [h] h ] & = +1 aligned and f(0)=2 From Eq. (i), we get array ll +0=2= +1 & - =1 array

Let f: R R be defined by f(x)= array ccc + [x] x , & if & x>0 2, & if & x=0 + [ x-x x^3 ], & if & x < 0 array . where, [x] denotes the integral part of x . If f continuous at x=0 , then - is equal to

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