If `f(x)={2x+b , (x lt a) and x+d , (x leq a)` is such that `Lt_(x->a) f(x)=I` then `I =`

If (x)={2x+b,(x

If f(x)=sqrt(x-2) , for 2 lt x lt 4 , then f(x) is

If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative of f(x) x=0

Consider the function f(x) =[(1-x,0 leq x leq 1),(x+ 2, 1 lt x lt 2),(4-x,2 leqxleq4)). Let lim_(x->1) f(f(x))= l and lim_(x->1) f(f(x))=m then which one of the following hold good ? (A) l exist but m does not (B) m exist but l does not (C) both exist (D) both does not exist

f(x)={x if x is rational -x if x is irrational then Lt_(x rarr0)f(x)=

Let f(x)={(-1, -2 leq x lt 0),(x^2-1, 0 lt x leq 2)) and g(x)= |f(x)|+f|x| then the number of points which g(x) is non differentiable, is (A) at most one point (B) 2 (C) exactly one point (D) infinite

If f(x) = {(x,",", x ge 0),(x^(2),",",x lt 0):} , then f(x) is

If a lt b lt c in R and f (a + b +c - x) = f (x) for all, x then int_(a)^(b) (x(f(x) + f(x + c))dx)/(a + b) is:

If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x le 2):} , then f is

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