UCSF 137 Lecture 18: UCSF 137 - Lecture 18 (1)

Describe all solutions of Ax =0 in parametric vector form, where A is row equivalent to the given matrix 1 0-2-54 8 00 1 0 02 x=x Type an integer or fraction for each matrix element.)

(1 point) A string of length L is secured at both ends. The string has no initial displacement, but has initial velocity f(z) at any point Choose the PDE and boundarylinitial conditions that model this scenario Select the partial differential equation that can be used to model this scenario A. k 00 Select ALL boundary/initial conditions that apply to this scenario A. u(L, t) = 0, t > 0 LU =f(x), OC, u(z,0) = L, =0, 00 at lt=0 OF. u(z, L) = f(x), 00 J, u(z, 0) = 0, K. L. M. u(0, t) L, 00 t > 0 t > 0 ON, u(0, t) = 0,

1. (16 pts) Sketch the graph of a function f satisfying all of the following conditions: (a) Domain of f = (-00, 0) U (0, +00); (b) f is even; (c) f is continuous on (0, +00); (d) f is not differentiable at x 4 ; e) lim f(x)=-3, lim f(x)=-00, (f) f'(x) > 0 on (0,4); (g) f'(x) 0 on (2,4) and (4, +o0)