Let`f:[1,oo)->R` and`f(x)=x(int_1^xe^t/tdt)-e^x`.Then (a) f(x) is an increasing function (b)` lim_(x->oo)f(x)->oo` (c) `fprime(x)` has a maxima at x=e (d) f(x) is a decreasing function

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

If f(x)=x^3+b x^2+c x+d and 0 le b^2 le c , then a) f(x) is a strictly increasing function b)f(x) has local maxima c) f(x) is a strictly decreasing function d) f(x) is bounded

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

Let f :RtoR be a positive, increasing function with lim_(xtooo) (f(3x))/(f(x))=1 . Then lim_(xtooo) (f(2x))/(f(x)) is equal to

If f(x)=int_(x^2)^(x^2+1)e^-t^2dt , then f(x) increases in (0,2) (b) no value of x (0,oo) (d) (-oo,0)

Let f(x)=int_(0)^(x)(e^(t))/(t)dt(xgt0), then e^(-a)[f(x+1)-f(1+a)]=

Let f be a real-valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) Prove that int_x^(x+8)f(t)dt is constant function.

If lm_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {{f(x)+(3f(x)−1)/(f_2(x))}=3 ,then the value of lim_(x->oo) f(x) is

If f(x)=xe^(x(x−1)) , then f(x) is (a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]

Let f:R to R be defined by f(x) =e^(x)-e^(-x). Prove that f(x) is invertible. Also find the inverse function.