`"I f"(x)={((e^x-1)xsinx)/(x^n),x >0 0,x=0` is derivable at `x=0` then interval of possible values of `' n '` is `[1,oo)` (b) `(-oo,1]` `(-oo,2]` (d) `[1,2]`

If f(n)=int_(0)^(2015)(e^(x))/(1+x^(n))dx , then find the value of lim_(nto oo)f(n)

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] .

If e^x+e^(f(x))=e , then the range of f(x) is (-oo,1] (b) (-oo,1) (1, oo) (d) [1,oo)

The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) (b) (-1,\ oo) (c) (-oo,\ oo) (d) (0,\ oo)

The interval of increase of the function f(x)=x-e^x+tan(2pi//7) is (a) (0,\ oo) (b) (-oo,\ 0) (c) (1,\ oo) (d) (-oo,\ 1)

The set of points where the function f(x)=x|x| is differentiable is (-oo,oo) (b) (-oo,0)uu(0,oo) (0,oo) (d) [0,oo)

The solution set of the inequality max {1-x^2,|x-1|}<1 is (-oo,0)uu(1,oo) (b) (-oo,0)uu(2,oo) (0,2) (d) (0,2)

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (-oo,1) and (2, 3). If f(1)= -8, then the range of f(x) is (a) [3,oo) (b) [-8,oo) (c) [-7,oo) (d) (-oo,6]

e^(2x)-(a-1)e^x-ageq0AAx in R , then values of a which satisfy are. (a) a in (-oo,0) (b) a in (-oo,0] (c) a in R (d) a in (-oo,2]