Use the function `f(x)=x^(1/x),x >0,` to determine the bigger of the two numbers `e^(pi)a n dpi^edot`

Consider the function f(x)={{:(xsin(pi)/(x),"for"xgt0),(0,"for"x=0):} Then, the number of points in (0,1) where the derivative f'(x) vanishes is

Let the function f(x)=x^2+x+s in x-cosx+log(1+|x|) be defined on the interval [0,1] .Define functions g(x)a n dh(x)in[-1,0] satisfying g(-x)=-f(x)a n dh(-x)=f(x)AAx in [0,1]dot

Show that the function f defined by f(x)= |1-x+|x|| , where x is any real number, is a continuous function.

Which of the following function is/are periodic? (a)f(x)={1,xi sr a t ion a l0,xi si r r a t ion a l (b)f(x)={x-[x]; 2n

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1) f(x) has two points of extrema

The period of the function f(x) = a^({ tan ( pi x) } +x -[x] ) , where a gt 0 , [x] denotes the greatest integer function and x is real number, is

The function f : [0,2 pi] to 1 [-1,1] defined by f(x) = sin x is

If f:[0,oo[vecR is the function defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2), then check whether f(x) is injective or not.

The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N , has a local minimum at x=pi/6 . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number