The possible values of a for which`e^(2x)-(a-2)e^x+a < 0,` for atleast one `x in (0,oo)`

Find the possible values of a such that f(x)=e^(2x)-(a+1)e^(x)+2x is monotonically increasing for x in R.

Set of all possible values of a such that f(x)=e^(2x)-(a+1)e^(x)+2x is monotonically increasing for all x in R is (-oo,a] ,then (a^(3))/(54) is

Find possible values of 'a' such that f(x) =e^(2x) -2(a^(2) -21) e^(x)+ 8x+5 is monotonically increasing for x in R.

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

If the exhaustive set of all possible values of c such that f(x)=e^(2x)-(c+1)e^(x)+2x+cos2+sin1f(x)=e^(2x)-(c+1)e^(x)+2x+cos2+sin1(-oo,lambda], then find the value of lambda

If sqrt(a+ib)=x+iy, then possible value of sqrt(a-ib) is x^(2)+y^(2) b.sqrt(x^(2)+y^(2)) c.x+iydx-iy e.sqrt(x^(2)-y^(2))

Let set of all possible values of lamda such that f (x)= e ^(2x) - (lamda+1) e ^(x) +2x is monotonically increasing for AA x in R is (-oo, k]. Find the value of k.

The value of a for which exactly one root of the equation e^(a)x^(2)-e^(2a)x+e^(a)-1=0 lies between 1 and 2 are given by

The value of a for which exactly one root of the equation e^(a)x^(2)-e^(2a)x+e^(a)-1 lies between 1 and 2 are given by