1. Consider the lamina with uniform density p bounded by the functions f(x) = 4-x and g(x) = 0, for 0 x 2 (i.e., the lamina is 1/4 of a circle of radius 2). pf(f(x) = g(x))x dx. (a) Find My for the lamina using the formula My = p. (b) Find M for the lamina using the formula M = (p/2) f(f(x)) ((g(x)) dx. (c) Find the center of mass of the lamina. 2. For each sequence, determine whether the sequence converges or diverges. If it converges, find the limit. Show your work. You may use these facts whitout proof: lim,00 VC = 1 (for any constant C > 0) and lim n = 1. (Everything else has to be proved.) (a) ak = (-1) (k + 1)e* n+1 (b) an=(-1)" n+n+1 3n+2 (c) an = 3n+n (d) a = (1+(1)) cos() (e) an=8+(-1)+1 + cos(n) (f) an= 22n+3 + n In(3 +2) (g) a = i Hint: use the Squeeze Theorem for the last two sequences.