Curve Packet for Chapter 3
Part A
dy
for the following using the limit definition of derivative. Show all work.
dx
2
2
2
1. y x 1
2. y x
3. y x 3
4. y 3x
Find
6.
y x
7.
yx
3
8.
y x 1
3
9.
y
5.
x 1
10.
y 2 x
y 5 x3
Part B
dy
for the following using the sym

Common Derivatives and Integrals
Derivatives
Basic Properties/Formulas/Rules d ( cf ( x ) ) = cf ( x ) , c is any constant. ( f ( x ) g ( x ) ) = f ( x ) g ( x ) dx dn d ( c ) = 0 , c is any constant. ( x ) = nxn-1 , n is any number. dx dx f f g - f g (Qu

Calculus Cheat Sheet
Integrals
Definitions Anti-Derivative : An anti-derivative of f ( x ) Definite Integral: Suppose f ( x ) is continuous on [ a, b] . Divide [ a, b ] into n subintervals of width D x and choose x from each interval.
* i
is a function, F

Tabular Integration by Parts
David Horowitz, Golden West College, Huntington Beach, CA 92647 The College Mathematics Journal, September 1990, Volume 21, Number 4, pp. 307311. Only a few contemporary calculus textbooks provide even a cursory presentation o

Intermediate Value Theorem
If f(1)=-4 and f(6)=9, then there must be a x-value
between 1 and 6 where f crosses the x-axis.
Average Rate of Change
Slope of secant line between two points, use to estimate
instantanous rate of change at a point.
Instantenous