The values of constants a and b so asmake the function `f(x)={1/([x]), |x| leq 1 and ax^2+b , |x| lt 1` continuous as well as differentiable for all x, are

The values of constants a and b so as to make the function f(x)={(1/|x|, |x|ge1),(ax^2+b, |x|lt1):} , continuous as well as differentiable for all x, are

The function f(x) ={{:(e^(2x)-1,","x lt 0),(ax+(bx^2)/2-,","xlt0):} continuous and differentiable for

Consider a function g(x)=f(x-2),AA x in R , where f(x)={{:((1)/(|x|),":",|x|ge1),(ax^(2)+b,":",|x|lt1):} . If g(x) is continuous as well as differentiable for all x, then

Consider a function g(x)=f(x-2),AA x in R , where f(x)={{:((1)/(|x|),":",|x|ge1),(ax^(2)+b,":",|x|lt1):} . If g(x) is continuous as well as differentiable for all x, then

The value of constants a and b, so that : lim_(x rarr oo) [(x^(2) + 1)/(x+1) - ax - b] = 0 , is :

Find "a" and "b" such that the function f(x)={3ax+b, if x>1 11 if x=1 is continuous. 5ax-2b, if x<1