Proof of Sum Rule By expressing u and v in terms of their com- ponents, prove that (u(t) + v(t)) = u'(t) + v'(t). dt

Consider a function z = F(u(s, t), v(s, t)) where F, u, and u are differentiable and u(8, 6) = -1, v(8, 6) = 2, u, (8, 6) = 5, u, (8, 6) = 9, vs(8, 6) = −3, v₁(8, 6) = 4, Fu(-1,2) = -4, and F(-1,2)= -10. Compute and when s = 8 and t = 6 dt

· Use integration by parts to evaluate (6xe*dx. -7x A) (7x+1)(6e7*) бе +C 49 B) -7x е +C 7 C) (6e7") -7x бе +C 49 D) x( 6e +C 7 E) -7x e +C 7

15)- Estimate f'(4),and f"(4) using central difference formulas of order o(h?) for the data (0,1), (2,4), (4,6), (6,9)