Math 152, Section 6.2Volumes
If a region in a plane is revolved about a line in a plane, the resulting solid is called a solid of revolution
and the solid is said to be generated by the region. The li
Math 152, Activity 7
Name:
1. Part A
1
With n 10, approximate sin( x 2 )dx, using the Simpsons rule.
0
Part B:
4
Determine f 4 x and graph y f x
From your graph, determine the maximum value of
f 4 ( x
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Complementaryangles
MATH 1401 SPRING 2000 CHEAT SHEET
FINAL
JAN MANDEL
1. Important formulas from algebra.
sin(a + b) = sin(a) cos(b) + cos(a) sin(b),
n m
b
(log a)b
2
2
sin2 x + cos
x = 1, ab+c = ab ac , am/n =
x1,2 =
b
Measurement Formulas
A graphical list of the formulas for measurement concepts. Print this page for
reference.
Shapes
Formula
Rectangle:
Area = Length X Width
A = lw
Perimeter = 2 X Lengths + 2 X Widt
Useful Inequalities
cfw_x2 > 0
version 0.10a August 1, 2011
n
X
CauchySchwarz
x i yi
i=1
n
X
Minkowski
i=1
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n
X
i=1
Bernoulli
!2
n
X
x2i
i=1
!1
xi + yi 
n
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xi yi 
xi p
!1/p
i=1
r
(1 +
Cheat Sheet for Geometry Midterm
(only includes official postulates, theorems, corollaries and formulas)
points, lines, planes, intersections,
Through any two points there is exactly one line.
Through
Mathematics Cheat Sheet for Population Biology
James Holland Jones,
Department of Anthropological Sciences
Stanford University
April 30, 2008
1
Introduction
If you fake it long enough, there comes a p
TRIANGLE:
Centers:
Incenter
Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection
of the angle bisectors of the triangle.
The radius of incircle is
Math 152, Activity 12(4 points)
Name:
1. Given the nth term, an, of an infinite sequence, find the first four terms and find if it exists,
limn an
a. a n 1 (1)n1
b. an
n 1
n
c. an
1
d. a n
1.001
n
l
Math 152, Section 5.9 Approximate integration
Example 1: Consider the function
f ( x) sin x 2
1
Using n 10, approximate sin( x 2 )dx and estimate the error in the approximation.
0
a. Using the Midpo
Math 152, Section 8.1Sequences
I.
An infinite sequence a1 , a2 , a3 , a4 , a5 ,. is a list of numbers written in a define order
Notation:
an or an n1
Example 1:
Write down the general nth term, an for
Math1XX3, Winter 2007
1. [6 marks] Find the solution to the differential equation dy = 6 y 2 sin( 2 x ) dx with the condition that y (0) = 1 / 6
2. [6 marks] Find the most general solution to the line
Math1XX3, Winter 2007
1. [6 marks] Find the solution to the differential equation dy = 6 y 2 sin( 2 x ) dx with the condition that y (0) = 1 / 6
The differential equation is separable 1 y 2 dy = 6 sin
Math 152Activity 9 (4 pts)
Name:
1. The base of a certain solid is the region of xy plane bounded by the equations y x 2 , y x . Every
crosssection perpendicular to the xaxis is a semicircle with d
MTH 132
2.8. Related Rates
Worksheet #7
Problem #1. (WW HW14 #4). Melting snowball.
A spherical snowball is melting in such a way that its diameter is decreasing at rate
of 3 cm/min. At what rate is t
Math 152, Section 6.1: More about Areas
I.
Area Between Two Curves
Consider region S that lies between two curves y f ( x) and y g ( x) and two vertical lines
x a and x b , where f and g are continuou
Math 152, Activity 8 (4 points) Name:
1.
Sketch the region bounded by the graphs of the given equations, show a typical vertical or
horizontal rectangle and find the area of the region bounded by th
Basic Differentiation Formulas
In the table below, ? 0 B and @ 1B represent differentiable functions of B
Derivative of a constant
Derivative of constant
multiple
Derivative of sum or
difference
.B
.