If f(x) is an even function, state whether f'(x) is an odd function or an even function.

Statement I Integral of an even function is not always an odd function. Statement II Integral of an odd function is an even function .

Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(hrarr0^(+))(f(a)-f(a-h))/(h) =lim_(hrarr0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(hrarr0^(+))(f(a+h)-f(a))/(h) =lim_(hrarr0^(+))(f(a)-f(a+h))/(h) =lim_(hrarr0^(+)) (f(a)-f(x))/(a-x) respectively. Let f be a twice differentiable function. We also know that derivative of a even function is odd function and derivative of an odd function is even function. If f is even function, which of the following is right hand derivative of f' at x=a?

If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x) , then f(x) is, (given f(0) = 0) a. an even function b. an odd function c. neither even nor odd function d. can't say

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and STATEMENT 2 : g(x)=f'(x) is an even function , then f(x) is an odd function.

Let f be an even function and f'(x) exists, then f'(0) is

Let f(x) =x and g(x)=|x| be two real-valued functions, check whether the functions are one -one.

If f is an even function, then find the realvalues of x satisfying the equation f(x)=f((x+1)/(x+2))

Is the function defined by f(x) = |x| a continuous function?