If x` =2` is a real root of cubic equations `f(x) =3x^3+ bx^2+ bx+3 =0` then the value of lim alue of `lim_(x->1/2)(e^(f(x))-1)/(2x-1)=`

If x=2 is a real root of cubic equation f (x) = 3x^(3)+bx^(2)+bx+3=0 . Then the value of lim_(xrarr(1)/(2)) (e^(f(x)-1)/(2x-1))

If alpha is a real root of the cubic equation ax^(3)+bx^(2)+bx+a=0, then the value of lim_(x rarr(1)/(a))(tan(ax^(3)+bx^(2)+bx+a))/((alpha x-1)) is

If (x^2+x−2)/(x+3) -1) f(x) then find the value of lim_(x->-1) f(x)

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

The value of lim_(x rarr(1)/(2))((f(x)+x-1)^(3))/((x-(1)/(2))) is

Let f(x)=(bx+a)/(x+1), lim_(x to 0)f(x)=2 then the value of a is .

If lim_(xrarr0)(1+ax+bx^2)^(2//x)=e^3 , then the value of a and b, is :

If f(x) is defined as f(x)={{:(2x+3,x,le 0),(3x+3,x,ge 0):} then evaluate : lim_(xrarr0) f(x) "and" lim_(xrarr1) f(x)

If the normal to the curve y=f(x) at x=0 be given by the equation 3x-y+3=0 , then the value of lim_(x rarr0)x^(2){f(x^(2))-5f(4x^(2))+4f(7x^(2))}^(-1) is (-1)/(k) then k =

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .