19. Integrationin ElemeneryTerms 377
Moreover, if a problem has been reduced to the integration of a rational function,
it is then certain that an elementary primitive exists, even when the difficulty
INTEGRALS
CHAPTER
"integral,"
the
The derivative does not display its full strength until allied with the
complete
topic
of
this
second main concept
Part III. At first
may seem to be a
digression-in t
last change: Sept 13, 2015
Eulers Formula
Math 220
Complex numbers
A complex number is an expression of the form
x + iy
where x and y are real numbers and i is the imaginary square root of 1. For exam
PART II:
VIII.3 : 13, 14
13. Let r > 0. Using Limit 3, prove the limit: lim 1 +
79
< 7
7
= e7
Hint: Let x = ry and let y .
14. Show that:
lim n
D9
E
a1
= log a
1
Hint: Let h =
n
This exercise sho
Homework 3
S212
Part 1:
VII. 2: 3, 5
Restrict f to an interval so that the inverse function g is defined in an interval containing the
indicated point, and find the derivative of the inverse fu
Homework 5
Part 1
IX.4: 4,5
Write out the lower and upper sums for the following functions and intevals. Use a
partition such that the length of each small interval is (a). , (b) 1/3, (c) , (d
Homework 7
XI.3: 1, 2, 5, 8, 14
1.
sin8 x dx . 2.
cos < x dx . 5.
8. 1 cos d and
E
14.
dx
I
x= y=
+
= 1.
4 16
1 + cos d
FGH
XI.3 Supplementary: 2, 4, 11, 16, 21
1
<
1 =
2. t
Homework 9
XII.2: 1, 8
Find the area enclosed by the following curves:
1. = 2 1 + cos 8. = 2 cos 3 ,
6
6
XII.2 Supplementary: 3
Find the areas of the following regions, bounded by the c