Can someone help with these and show how you got to the answer?

. If f (x) = e'i'i'x , evaluate a. [1'00]2 b- FIX) 9- \"TIMI2 01- 1/f(x) . Rewrite the following expressions in the form a + 1?) , where a and b are real numbers: 1' a. B b. 2" c. 1110') d. ii . Write down the general solutions to the differential equation: 2 3%}: (x) = c2f(x) , where c is a real number. 4. Find an example of a unit vector that is orthogonal to the Cartesian vector 3i + I + 2E. [Note that E, j and E are unit vectors that lie along the Cartesian x, y, and z axes, respectively.] . Given a normalized probability density function P(x) of nding the variable x in the interval [x, x + dx], write the denition for a) the mean value (x), b) the variance 02 = ((x - (x))2), and c) the standard deviation of the variable x