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)`

f(x)=int(2-(1)/(1+x^(2))-(1)/(sqrt(1+x^(2))))dx then fis (A) increasing in (0,pi) and decreasing in (-oo,0)(B) increasing in (-oo,0) and decreasing in (0,oo)(C) increasing in (-oo,oo) and (D) decreasing in (-oo,oo)

The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,pi/e), decreasing in (pi/e ,oo) decreasing in (0,pi/e), increasing in (pi/e ,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)

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)

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)

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)

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

The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,(pi)/(e)), decreasing in ((pi)/(e),oo) decreasing in (0,(pi)/(e)), increasing in ((pi)/(e),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)