MATH 253 2010 Midterm 2 Version D Solutions -...

Calculus II Midterm 2 March, 2010 2
1. (3 marks each; total 12 marks) Answer each question in the space provided. You
MUST show your work.
a) Given the parametric equations
t x 2 5 + =
,
1 9 6
2
+ + = t t y
find
dx
dy
evaluated at the point (7, 16).
b) Consider a 60 L tank filled with water, initially containing 0.03 kg of salt per litre.
Water containing 0.1 kg/L of salt flows into the tank at the rate of 5 L/min. If the
salt-water solution in the tank is thoroughly mixed and flows out from the tank at
a rate of 5 L/min, then set up the differential equation describing the rate of
change of salt (call it A ) in kg in the tank as a function of time (call it t ) in
minutes, and state the corresponding initial condition. You do NOT have to solve
the equation.
c) If
uvw w v w u w v u f 5 3 cos ) , , ( 4 2 + + =
, find
v
d) For what nonzero values of k does the function
kt B kt A y cos sin + =
satisfy
the differential equation
0 4 = +
′ ′
y y
? State all possible values.
f