If X(t) is periodic, then its auto correlation function is also periodic

Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) = 2ex, a = -0.01 Set the center of the linearization as x = ...

2) Use the Chain Rule to express the second derivative of fog in terms of the first and second derivatives of ƒ and g.

Assume that h[n]=(-1)"g[n]. What is the relation between H(Z) and G(z) O Hz) = (- 1)" G(z) H(2) =G((-1)"z) O HZ) =G(-z) O HZ) =G(z-1) OHZ) =G(z – T) OH2) = 1/G(z) None of the above.

A table of values for f, g, f', and g is given below. x | f(x) g(x) | f'(x) g(x) 1 2 1 2 3 2 1 3 1 1 3 3 3 1 (A) If h(x) = f(g(æ)), then h'(3) = (B) If H(x) = g(f(x)), then H'(3) =

Let P(t) represent the price of a share of stock of a corporation at time t. What does each of the following statements tell us about the signs of the first and second derivatives of P(t)? (Hint - you might want to sketch a possible graph.) (a) The price of the stock is rising faster and faster. The sign of dP dt is ---Select--- v The sign of (b) The price of the The sign of The sign of d²p dt² is --Select--- ✓ stock is close to bottoming out. dP dt d²p dt² is ---Select--- ✓ is ---Select--- ✓

Determine whether the given set of functions is linearly independent on the interval (-, ). fi(x) = 3, f2(x) = cos²(x), f3(x) = sin? (x)

Let fand g be the functions whose graphs are shown below. -4-3-2 4- 3 2 1 -1- -2 -3- -4- N f(x) 2 3 4 X g(x) (a) Let u(x) = f(x)g(x). Find u'(4). (b) Let v(x) = g(g(x)) . Find v'(-3). 10 5

Consider the discrete-time dynamical system xt+1 = 5xt(1-xt).If xt = 4/5, xt +1 = _____Is x1 = 4/5 an equilibrium for this system? ______Write the updating function rule as f(x) = 5x(1-x).Compute the derivative: f'(x) = ______Evaluate the derivative at the equilibrium: ___________Is the equilibrium stable, unstable or neither? ________