Consider the following initial value problem: y"+14y' + 74y = h(t); y(0) = 0, y'(0) = 5; 74, h(t) = >= {21 2/5 (a) Sketch the graph of the forcing function on an appropriate interval. 80 + 79 78 77- 76 75 74- 73 72 71 70 4 (b) Find the solution of the given initial value problem. NOTE: Denote the two Heaviside functions by u(t) and us(t). Indicate separately the values of c and d knowing that c is the minimum of the two values. |y(t) =

3. Determine whether the function is even, odd or neither. (a) (b) g(x) = |r| + x² y = f(x); 4. Let f(r) = |x – 2|, g(x) = 3x +1 and the graph of h(x) is given. %3D y y=h(x) -5 Find (b) ) (-2) ()« (a) (f + g)(x) = (c) (goh)(3) = (d) (f o g)(x) = (e) (ho h)(2) =

8. Find all discontinuities of f(x) = x²2x-3 and label them as removable or nonremovable.