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

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)dot

Show that the function f(x)=x^2 is a strictly decreasing function on (-oo,\ 0) .

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

Show that the function f(x)=x^2 is strictly increasing function on (0,\ oo) .

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then: (a) g is increasing on (1,oo) (b) g is decreasing on (1,oo) (c) g is increasing on (1,2) and decreasing on (2,oo) (d) g is decreasing on (1,2) and increasing on (2,oo)

Prove that the function f(x)=(log)_a x is increasing on (0,oo) if a >1 and decreasing on (0,oo), if 0ltalt1

Prove that the function f(x)=(log)_e x is increasing on (0,\ oo) .

Without using the derivative, show that the function f(x)=|x| is (a) strictly increasing in (0,\ oo) (b) strictly decreasing in (-oo,\ 0)