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 this chapter derivatives do not appear even once! The st
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 example,
2 + 3i is a complex number. Just as we use the sym
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 shows how approximations of the log can be obtained by tak
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 function at the indicated point.
3. f x = x E -x + 5
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) 1/n
4. f x = x $ in the interval 0,2
3
3
5. Le
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 curve given in polar coordinates:
3. =
1 cos ()
XII.3:
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 or
impossibility of finding the factors of the denomin