`L e tf(x)={x+2 , x <-1 ; x^2 , -1 lt= x < 1 and (x-2)^2 , x geq 1` Then number of times `f^(prime)(x)` changes its sign in `(-oo,oo)` is___

L e tf(x)={x+2,x<-1x^2,-1lt=x<1(x-2)^2,xgeq1 Then number of times f^(prime)(x) changes its sign in (-oo,oo) is___

3x - 2 lt 2x + 1

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

f (x)= {{:(2(x+1),,, x le -1),( sqrt(1- x^(2)),,, -1 lt x lt 1), (|||x|-1|-1|,,, x ge1 ):} , then:

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 ,

y = cos ^(-1)((2x)/(1 +x^(2))),-1 lt x lt1 . find dy/dx

Let f(x)={1+(2x)/a ,0lt=x<1 and ax ,1lt=x<2 If lim_(x->1)f(x) exists ,then a is (a) 1 (b) -1 (c) 2 (d) -2

If f(x) = { x, 0 lt x lt 1/2, 1/2, x = 1/2, 1-x , 1/2 lt x lt 1} and g(x) = (x-1/2)^2 then find the area bounded by f(x) and g(x) from x = 1/2 to x= sqrt3/2

0 lt a lt 2 pi , sin^(-1)(sin a ) lt x^(2)-2x for all x in I then a in