. Let f: RR be defined by sin[x] a + , if x > 0 х 2 if x=0 where [x] sin x - x B+ ,if x<0 3 denotes the integral part of x. If f continuous at x = 0, then ß-a = [EAM - 2012] 1) -1 1 3) O 4) 2 21

Let f :R-> R be defined by f(x)={(alpha+sin[x]/x,if x>0 ),(2,if x=0),(beta+[(sinx-x)/x^3],if x<0):} where [x] denotes the integral part of x. If f continuous at x = 0 , then beta-alpha =

Let f:RrarrR be function defined by f(x)={(sin(x^2)/2, ifx!=0),(0,if x=0):} Then, at x=0, f is

Let f(x)=sin x,x =0 then

Determine if f defined by f(x)={x^2sin1/x , if""x!=0 0, if""""x=0

Let f:R rarr R be defined by f(x)={x+2x^(2)sin((1)/(x)) for x!=0,0 for x=0 then

Is f defined by f(x) = {((sin 2x)/x, if x != 0),(1, if x = 0):} continuous at 0?

Let f: RR to RR be a function defined by f(x)={{:([x],x le2),(0,x gt2):} , where [x] is the greatest integer less than or equal to x. If I=int_(-1)^(2)(xf(x^(2)))/(2+f(x+1))dx , then the value of (4I-1) is-