Consider the differential equation d2 dx2 + = 0. Determine the eigenvalues (and corresponding eigenfunctions) if satisfies the following boundary conditions. Analyze three cases ( > 0, = 0, < 0). You may assume that the eigenvalues are real. (a) (0) = 0 and ()=0 *(b) (0) = 0 and (1) = 0 (c) d dx(0) = 0 and d dx(L) = 0 (If necessary, see Section 2.4.1.) *(d) (0) = 0 and d dx(L)=0 (e) d dx(0) = 0 and (L)=0 *(f) (a) = 0 and (b) = 0 (You may assume that > 0.) (g) (0) = 0 and d dx(L) + (L) = 0 (If necessary, see Section 5.8.)

Math 103 Week E 02/05 02/05 Hill Huntington (1941 Apportionment Act) 1) Compute the md 2) Compute the mQ a) [mQ=states population/md] 3) Round each mQ using the rule a) The cutoff for rounding numbers is c=√ LU b) The Geometric Mean determines the rounding for a number 4) Give this amount of seats to each state Arithmetic Mean: Directly in the...