A function `f:R rarrR` is defined as `f(x)=lim_(nrarroo) (ax^(2)+bx+c+e^(nx))/(1+c.e^(nx))` where f is continuous on R, thenA. point (a, b, c) lies on line in spaceB. point (a, b) represents the 2-dimensional Cartesian planeC. Locus of point (a, c) and (c, b) intersect at one pointD. point (a, b, c) lies on the plane in space

A function `f:R rarrR` is defined as `f(x)=lim_(nrarroo) (ax^(2)+bx+c+

1.	A function `f:R rarrR` is defined as `f(x)=lim_(nrarroo) (ax^(2)+bx+c+e^(nx))/(1+c.e^(nx))` where f is continuous on R, thenA. point (a, b, c) lies on line in spaceB. point (a, b) represents the 2-dimensional Cartesian planeC. Locus of point (a, c) and (c, b) intersect at one pointD. point (a, b, c) lies on the plane in space
Answer» Correct Answer - A::B::C `f(x)=underset(nrarroo)(lim)(ax^(2)+bx+c+e^(nx))/(1+c.e^(nx))` `={{:(underset(nrarroo)(lim)(ax^(2)+bx+c+(e^(x))^(n))/(1+c.(e^(x))^(n)),,xlt0),(underset(nrarroo)(lim)(ax^(2)+bx+c+(e^(x))^(n))/(1+c.(e^(x))^(n)),,x=0),(underset(nrarroo)(lim)((ax^(2)+bx+c)/((e^(x))^(n)))/((1)/((e^(x))^(n))+c),,xgt0):}` `={{:(ax^(2)+bx+c,,xlt0),(1,,x=0),((1)/(c),,xgt0):}` since f(x) is continuous function `AA x in R` `therefore" "underset(xrarr0^(+))(lim)f(x)=underset(xrarr0^(-))(lim)f(x)=f(0)` `rArr" "underset(xrarr0^(+))(lim)((1)/(c))=underset(xrarr0^(-))(lim)(ax^(2)+bx+c)=1` `rArr" "(1)/(c)=1=c rArr c=1` `therefore " "c=1, a, b in R`