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The answers to the final exam of math 251, a college-level mathematics course, which was held on december 20, 2007. The exam covers various topics including algebraic equations, differential equations, and eigenvalues. Students can use this document to check their solutions and review the correct answers.
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Final Exam
December 20, 2007
(b) S(t) = (5000 − 10k) e
t (^) /
(c) 1
1 / 2 1 / 2
1 / 2
e e
e k
2 , n = 1, 2, 3, … ; the corresponding eigenfunctions
are (any nonzero multiple of) Xn = sin(2nx), n = 1, 2, 3, …
(a)
(b) X(0) = 0 and X ′(4) = 0
∞
=
1
sin(( 2 1 ) ) ( 2 1 )
n
n x n
f x
(b) It converges to 0.
− −
2 cos 3
( ,) 10 4 cos
20 2 / 9 802 / 9 x e
x u xt e
(b) lim ( , )= 10 → ∞
ux t t
