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

Show that f(x)=(1)/(x) is a decreasing function on (0,oo)

Show that f(x)=(1)/(x) is decreasing function on (0,oo)

Let f be the function f(x)=cos x-(1-(x^(2))/(2))* 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)

Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary.If F(x)=int_a^(x^3) g(t)dt, the F(x) is (A) an incresing function in R (B) an increasing function only in [0,oo) (C) a decreasing function R (D) a decreasing function only in [0,oo)

The function f(x)=x^(9)+3x^(7)+64 is increasing on (a) R(b)(-oo,0)(c)(0,oo) (d) R_(0)

Let f:(0,oo)vec R be given by f(x)=int_((1)/(x))^(x)(e^(-(t+(1)/(t)))dt)/(t), then (a)f(x) is monotonically increasing on [1,oo)(b)f(x) is monotonically decreasing on (1,oo)(b)f(x) is an odd function of x on R

Let f:R rarr R be a positive increasing function with lim_(x rarr oo)(f(3x))/(f(x))=1 then lim_(x rarr oo)(f(2x))/(f(x))=

Let f(x) is a differentiable function everywhere and suppose lim_(x rarr oo)(f'(x)+3f(x))=12 then lim_(x rarr oo)f(x) is equal to

Prove that the function f(x)=(log)_(e)x is increasing on (0,oo)

Prove that the function f(x)=log_(e)x is increasing on (0,oo)