Homework 7-due March 19th
Homework Problems
1. A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter of water enters the
tank at a rate of 5L/min. Brine that contains 0.04kg of salt per liter of water enters the tank at a rate
10L/min. the solution is kept thoroughly mixed and leaves the tank at a rate of 15L/min. How much
salt in the tank
(a) after t minutes
(b) what happens in the long run.
Remark: Both brines enter the tank at the same time.
2. Find the solution of the differential equation that satisfies the given initial condition.
p
ln (x3 (y 2 + 1)) − 2 ln ( (y 2 + 1)x)
dy
=
,
y(1) = 2 (initial condition)
dx
yx
3. Find the limit of the following sequences if it exists
√
(a) an = n 2n + 4n + 5n
(b) an =
3n
n+n! ,
where n! = 1 · 2 · · · n
Hint: In both parts (a) and (b) use the Squeeze Theorem
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