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)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a) -1 (b). 1 ( c.) 0 (d). 2

Discuss the continuity of f(x)={x{x}+1,0lt=x<1 and 2-{x},1lt=x<2 where {x} denotes the fractional part function.

Let f(x)={:{(x+1,x gt 0),(x-1,x lt 0):}

f(x) = (2x^(2) + 3)/(5), for oo lt x le 1 = 6 -5x, for 1 lt x lt 3 = x-3, for 3 le x lt 8, then

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___

f(x)={(x,0,le,x,le,1),(2x,-,1,1,lt,x,le,2):} then f'(1^(-)) is :

Let f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a ne 0 , then

If f(x)=Cx^(2), o lt x lt 2 is the p.d.f. of x then c is

3x-2 lt 2x+1