University of Washington
Math 125B, Summer 2014
June 26, 2014
Calculus with Analytic Geometry II: Syllabus
Instructor:
Oce:
Email:
Oce Hrs:
Christian Rudnick
C-113 Padelford Hall
rudnickc@math.washington.edu
Wednesday 10:50-11:50 am in my oce
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Math 125B, Summer 2014
Quiz 2: Solutions
Page 1 of 1
1. (5 points) Find the derivative of the function.
7x
g(x) =
6x
7x
d
dx
We have used that
b
a
u2 1
du,
u2 + 1
6x
7x
0
f (u)du =
Hint:
6x
u2 1
d
du =
2 +1
u
dx
7x
f (u)du +
6x
f (u)du
0
u2 1
d 7x u2 1
du
Math 125B, Summer 2014
Quiz 1: Solutions
Page 1 of 1
1. (5 points) Use the denition to nd an expression for the area under the graph of f (x) as a limit. Do
not evaluate the limit.
f (x) = x2 + 1 + 2x,
1x3
First, note that x = ba = 31 = 2 and xi = a + ix
Math 125B, Summer 2014
Quiz 3: Solutions
Page 1 of 1
1. (5 points) Find the area of the region that is bounded by y = 7x x2 from above and y = 2x from
below in the interval [0, 5]. Both curves do not intersect in between the endpoints of this interval.
Th
Math 125B, Summer 2014
Quiz 5: Solutions
Page 1 of 1
1. (5 points) Evaluate the integral.
x4
dx
x2 5x + 6
Since x2 5x + 6 = (x 2)(x 3), we see that
x4
x2 5x + 6
=
x4
A
B
=
+
.
(x 2)(x 3) x 2 x 3
Multiply through by the denominator on the left hand side to
Math 125B, Summer 2014
Quiz 6: Solutions
Page 1 of 2
1. (3 points) Set up, but do NOT compute the arc length of the curve, L.
0x
y = ln(cos x),
Since y =
sin(x)
cos(x)
4
= tan(x),
4
L=
1 + tan2 (x)dx
0
2. (7 points) Compute the, centroid of the region bo
Math 125B, Summer 2014
Quiz 0: Solutions
Page 1 of 1
1. Decompose g(x) = sin(x5 ) explicitly into two simpler functions g(u) and u(x) such that g(x) = g(u(x)
and compute the derivative g (x).
Take g(u) = sin(u) and u(x) = x5 . Then
dg dg du
=
= cos(u)5x4
Math 125B, Summer 2014
Quiz 4
Page 1 of 2
1. (5 points) An aquarium 4 m long, 3 m wide, and 2 m deep is full of water. Find the work needed to
pump half of the water out of the aquarium. (Use the fact that the density of water is 1000 kg/m3 , and
use 9.8