If `f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x)` then `f(x)` (a)increase in `(0,oo)` (b)decrease in `[0,oo]` (c)neither increases nor decreases in `[0,oo]` (d)increase in `(-oo,oo)`

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,3a) decreasing in (3a, 4a) (b). increasing in (a, 4a) decreasing in (5a ,oo) (c). increasing in (0,4a) (d). none of these

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)

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)

Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f decreases on [1,oo] (c) f has a minimum at x=1 (d) f has neither maximum nor minimum

Show that f(x)=1/(1+x^2) decreases in the interval [0,oo) and increases in the interval (-oo,0]dot

Show that f(x)=1/(1+x^2) decreases in the interval [0,\ oo) and increases in the interval (-oo,\ 0] .

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

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

If f(x)=(|x-1)/(x^2) the f(x) is one-one in (2,oo) b. one-one in (0,1) c. one-one in (-oo,0) d. one-one in (1,2)