Determine f(0) so that the function f(x) defined by f(x) = (4x-1)^{3} / [sinx/4 log(1+x^{2}/3) becomes continuous at x=0.

If f(x)=x+|x|+cos([π2]x) and g(x)=sinx, then which of the following option is INCORRECT ? (where [.] denotes the greatest integer function)

If f(x)=⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩(4x−1)3sin(xa)ln(1+x23),x≠09(ln4)3,x=0 is continuous at x=0, then the value of a is

If f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪⎩(4x−1)3sin(xa)log[1+(x23)],x≠09(log4)3,x=0 is a continuous function at x=0, then the value of a is equal to