Key to the Practice Final

Problem 1

A.  1/3 x e^-3x - 1/9 e^-3x + C

B.  1/2 sin^-1(x/3) + x/12 sqrt(9 - x²) + C

C.  -1/p e^cos(px) + C

D. 1/2 ln|x| - 1/5 ln|1 - x| - 2.3 ln|4 + x| + C

E.  3sin(x/3) - sin³(x/3) + C

F.  1/10 (e^3x sinx + 3e^3x cosx) + C

G.  (x + 3)^1/3 (-1/x² ln(x + 3) + 1/x(x + 3))

H.  e^-1

Problem 2

3921 pounds

Problem 3

A.  259

B.  76

C.  2.58

Problem 4

A.  dy/dt = ky

B.  7000 years old

Problem 5

80,000 mile tons

Problem 6

A.  False, let f(x) = g(x) = 1/x

B.  True, by the change of base formula the inside is a constant