4.6: Related Rates
Greg Kelly, Hanford High School, Richland, Washington
First, a review problem: Consider a sphere of radius 10cm.
If the radius changes 0.1cm (a very small amount) how much does the volume change?
4 V r3 3
dV 4 r 2dr
dV 4 10
5.3 Definite Integrals and Antiderivatives
Greg Kelly, Hanford High School, Richland, Washington
Page 269 gives rules for working with integrals, the most important of which are:
b
1.
a a
f x dx
a b
f x dx
Reversing the limits changes the sig
5.2 Definite Integrals
Greg Kelly, Hanford High School, Richland, Washington
3
V
2
1 2 t 1 8
When we find the area under a curve by adding rectangles, the answer is called a Rieman sum. The width of a rectangle is called a subinterval.
1
0
1
5.1 Estimating with Finite Sums
Greenfield Village, Michigan
Photo by Vickie Kelly, 2002 Greg Kelly, Hanford High School, Richland, Washington
Consider an object moving at a constant rate of 3 ft/sec. Since rate . time = distance:
3t
d
If we dra
MAT115
Quiz 5.
Name: 10:00 11:50 1:00 12:50 3:00 4:50
Circle the section of 115 that you attend:
The following quiz is due absolutely no later than 5:30 p.m. on Thursday, March 13 (2008). Once I have left my office at that time no papers will
Calculus Cheat Sheet
Derivatives
Definition and Notation f ( x + h) - f ( x) . If y = f ( x ) then the derivative is defined to be f ( x ) = lim h 0 h If y = f ( x ) then all of the following are equivalent notations for the derivative. df dy d f