PHYSICS 306
HOMEWORK #5
Due October 12, 2012
ALL PROBLEMS ARE WORTH 10 POINTS
1. (a) Verify the following integral
1
f (x, a)
a
ex
2 /a2
dx = 1
(b) Show that the function (x) dened by
(x) = lim f (x, a)
ao
has the property that (x) = o when x = o. (x) i
PHYS 306 HW 1 Solution
This document is meant to be a guide only. ALL missing steps must be shown in HW.
g (x)Df (x) f (x)Dg (x)
:
g (x)2
Beginning from rst principles for the derative:
1. Show D[f (x)/g (x)] =
D[f (x)/g (x)]
=
lim
f (x+x)
g (x+x)
f (x)
g
PHYS 306 HW 4 Solution
This document is meant to be a guide only. ALL missing steps must be shown in HW.
1. [P2.2.3] a) Use substitution y =
1
e
x and dy =
1
x
1
ey 2ydy = 2 (yey |1
0
dx =
0
1 1/2
1
x
dx =
dx
2
2y
ey dy ) = 2
0
0
4
b) Use the substitutio
PHYS 306 HW 3 Solution
This document is meant to be a guide only. ALL missing steps must be shown in HW.
1. [Q1] Find the anti-derivatives F(x). You must explicitly dierentiate to obtain f(x):
arctan( x )
a
a
1
d) F (x) = (x sin x cos x)
2
a) F (x) = x ln
PHYS 306 HW 2 Solution
This document is meant to be a guide only. ALL missing steps must be shown in HW.
1. [P1.6.3] (a) Beginning with the initial denition for the rule of 72: given a principle value p = 100,
after n = 2 years at growth rate r = 6%, you