The function `f(x)=x^x` decreases on the interval (a) `(0,\ e)` (b) `(0,\ 1)` (c) `(0,\ 1//e)` (d) `(1//e ,\ e)`

The function x^x decreases in the interval (a) (0,e) (b) (0,1) (c) (0,1/e) (d) none of these

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)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

The value of the integral int_0^1e^x^2_dx lies in the interval (a) (0,1) (b) (-1,0) (c) (1, e) (d) none of these

The mean value of the function f(x)= 2/(e^x+1) in the interval [0,2] is

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x))a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) ((e-1)/2,e-1) (d) (0,(e-1)/2)

The domain of f(x) is (0,1) Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

f(x)=|x log_e x| monotonically decreases in (0,1/e) (b) (1/e ,1) (1,oo) (d) (1/e ,oo)

The domain of f(x) is (0,1) .Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

The domain of f(x) is (0,1)dot Then the domain of (f(e^x)+f(1n|x|) is a. (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)