Maths 166 Review Sheet II
9
1. Approximate 1 ln 3x dx by the following methods each with n = 4, The Midpoint rule, The
Left Endpoint Riemann Sum, The Right Endpoint Riemann Sum, The Trapezoid rule, Simpsons Rule.
2. How large should you take n so that the
Math 166 Final Exam Review
9. A tank contains 100 L of pure water. Brine
that contains .1 kg of salt per liter of water enters the tank at a rate of 10 liters per
minute. The solution is kept mixed and exits the tank at the same rate. How much
salt is in
Math 166 Exam III Review
10. Give the integral (you do not have to evaluate it) that represents the arclength of the
curve x = 2 + t2 , y = cos t + t5 , 1 t 3.
1. For the following power series, nd the radius and interval of convergence.
11. Give the inte
Maths 166 Lab 2 - Solutions
Please email the completed file to me at [email protected] and make sure
each group member saves all working copies of the file as well. In
fact, you should always save your work often since computers tend to crash. We will
w
Maths 166 Lab 1- Stankewitz
Please email the completed file to me at [email protected] and make sure each group member saves all working copies of the
file as well. In fact, you should always save your work often since computers
work on it in class and
Math 166 Final Exam Review Solutions
1. Here = 1, 000 kg/m3 and g = 9.8 m/s2 .
a)
b)
100
3 g
50
3 g
c) part (a), yes.
d)
e)
160
3 g
140
3 g
2. M = 21 m = 23, x = 21/23
3. My = 6, Mx = 29, m = 10,
(, y ) = (3/5, 29/10)
x
24
4. (, y ) = ( 4(21) , 4(1 )
x
Maths 166 Exam I Review
1
over the
x1
interval [2, 5] and nd a value c such that f (c)
equals the average value.
22.
dx
(x 1)(x + 2)
1. Find the average value of f (x) =
sin( x) dx
2.
2
3.
1
6x
dx
4x2 + 2
4.
x3 4x4 9 dx
5.
x2 e1x dx
3
23.
24.
25.
dx
1)
x