If `f(x)={x^2sin(pix)/2,|x|<1x|x|,|x|geq1,t h e nf(x)i s` an even function (b) an odd function a periodic function (d) none of these

If f(x)={("sin"(pix)/2,, x lt1),(4x-3,,1lexle2),(log2(2x^(2)-4),,2ltxlt3):} then value of lim_(xto1)f(x)+lim_(xto2^(+))f(x) is

A function f(x) given by f(x)={{:(x^(2)sin""(pix)/(2), |x| lt1),(x|x|,|x| ge1):}is

Let f(x)={{:(x^(2) sin ((pix)/(2)),-1 lt x lt 1, x ne 0),(x|x|, x gt 1 or x le -1):} . Then ,

Let f:RrarrR be defined as f(x)={{:(2sin(-(pix)/2)",",if xlt-1),(|ax^2+x+b|",",if -1lexle1),(sin(pix)",",if xgt1):} If f(x) is continuous on R , then a+b equals

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

If f(x) = {((3sin pix)/(5x), ",",x != 0),(2k, ",",x = 0):} is continuous at x = 0, then the value of k is equal to

If f(x) = A sin ((pix)/(2)) + B and f'((1)/(2)) = sqrt(2) and int_(0)^(1)f(x) = (2A)/(pi) , then what is the value of B ?