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Algebra review (preparing for chapter 2):
(
a
2
–
b
2
)/(
a
–
b
) =
a
+
b
(
a
3
–
b
3
)/(
a
–
b
) =
a
2
+
ab
+
b
2
(
a
4
–
b
4
)/(
a
–
b
) =
a
3
+
a
2
b
+
ab
2
+
b
3
(
a
5
–
b
5
)/(
a
–
b
) =
a
4
+
a
3
b
+
a
2
b
2
+
ab
3
+
b
4
etc.
(
a
+
b
)
2
= 1
a
2
+ 2
ab
+ 1
b
2
(
a
+
b
)
3
= 1
a
3
+ 3
a
2
b
+ 3
ab
2
+ 1
b
3
(
a
+
b
)
4
= 1
a
4
+ 4
a
3
b
+ 6
a
2
b
2
+ 4
ab
3
+ 1
b
4
(
a
+
b
)
5
= 1
a
5
+ 5
a
4
b
+ 10
a
3
b
2
+ 10
a
2
b
3
+ 5
ab
4
+ 1
b
5
etc.
The coefficients in the polynomials to the right of the equal
signs are given by the entries of an array of numbers
discovered by the ancient Chinese, called Pascal’s triangle:
1
1
1
1
2
1
1
3
3
1
1
4
6
4
1
1
5
10
10
5
1
etc.
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View Full Document Chapter 2
Main point of 2.1? …
..?.
.
Limits of the form lim
h
→
0
(
f
(
x
+
h
) –
f
(
x
))/
h
, called
derivatives
, play a unifying role; they let us talk about
things like “slope of the tangent line” and “instantaneous
velocity” in a single common framework.
Example 1: Let
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This note was uploaded on 02/13/2012 for the course MATH 141 taught by Professor Staff during the Fall '11 term at UMass Lowell.
 Fall '11
 Staff
 Calculus, Algebra

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