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((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a))])/(a-x) for x < a, then f(a^-)<0 b. f has a removable discontinuity at x=a c. f has an irremovable discontinuity at x=a d. f(a^+)<0

If f(x)={(sin(x^(2)-3x),xle0 .^x+5x^(2),xgt0

Discuss the differentiability of f(x)= {( x sin(ln x^2),x!=0),( 0,x=0):} at x=0

Find the period of f(x)=sin((pix)/(n !))-cos((pix)/((n+1)!))

f(x)={cos(pix)/2,x >0 x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

f(x)={cos(pix)/2,x >0x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

Let f(x)=log(2x-x^2)+sin(pix)/2dot Then which of the following is/are true? Graph of f is symmetrical about the line x=1 Maximum value of f is1. Absolute minimum value of f does not exist. none of these

Find the range of f(x)=(2sin^2x+2sinx+3)/(sin^2x+sinx+1)

If f(x)=[2x]sin3pix then prove that f'(k^(+))=6kpi(-1)^(k) , (where [.] denotes the greatest integer function and k in N).