3. Find the derivative of h(x) =
p
x
.
x+1
solution: We use the quotient rule:
p
p
( x)0 (x + 1) (x + 1)0 ( x)
0
h (x) =
(x + 1)2
1
x 1/2 (x + 1) (x1/2 )(1)
= 2
(x + 1)2
1 1/2
x + 1 x 1/2 x1/2
2
= 2
(x + 1)2
1 1/2
x + 1 x 1/2
2
2
=
(x + 1)2
4. Let f (x) =
Summary By:Waheed Ashiru
This video shows how coordinate grid systems have been used
throughout history for navigation, archaeology, and space exploration.
Also included is a segment on how coordinate systems used by
computers differ from the Cartesian sy
Unit 5 Pages 676 680 Waheed Ashiru
Complete problems #2, 4, 9, 13, 17, 23, 25, 33, 39, 46
2.A sector of a circle is a bound by an arc and the two radii to the arcs endpoints.
4.two arcs of a circle with exactly one point in common are adjacent arcs.
9.a=1
1. After you have your math worked out on scratch paper, go back and verbally describe the steps you
took to evaluate the expressions. Make sure to use each of the vocabulary words at least once in your
writing.
o Did you notice anything interesting about
1. Write your birth date or the birth date of someone in your family as mm/dd/yy. April 23, 1972
o Now let a = the one- or two-digit month number,
o b = the negative of the one- or two-digit day number, and
o c = the two-digit year number.
(Our example: a
% Analyze Binary Learners of an ECOC Classifier
% ECOC models are an ensemble of strong classifiers. It might be helpful
% to inspect the performance of each binary classifier.
%
% Load and inspect the |arrhythmia| data set. Remove observations from the
%
% ANOVA with Multiple Responses
% Load Sample Data
% Load the sample data.
% Copyright 2015 The MathWorks, Inc.
load carsmall
whos
% Grouped plot matrix of four variables
% Create a grouped plot matrix of these variables using the gplotmatrix
% function.
% Analyze Images Using Linear Support Vector Machines
% This example shows how to determine which quadrant of an image a shape
% occupies by training an error-correcting output codes (ECOC) model comprised
of
% linear SVM binary learners. This example als
% Archimedean Copulas
% Find the rank correlation for a Gaussian or t copula with linear correlation
parameter of 0.8
% Copyright 2015 The MathWorks, Inc.
tau = copulastat('Gaussian',.8 ,'type','kendall')
% Find the Clayton copula parameter that correspon
Part 1
How do you find the circumference of a circle?
The circumference of a circle can be found by multiplying 3.14 by the diameter of the circle.
What information do you need in order to find the area or circumference of a circle?
You need to know the r
You will turn in the results of this activity for your assessment for this lesson.
Length= 8 inches
Width= 3 inches
Height= 12 inches
New cereal box
First cereal box
Length =16inches
Length=8inches
Width=6 inches
Width=3inches
Height=3 inches
Height=12 in
2. Not every function is dierentiable everywhere. In fact, you cant take the derivative
at points
of discontinuity,
with corners,
or with vertical tangents.
Note that saying that a function isnt dierentiable at points of discontinuity is equivalent to
dy
dy dv
=
dx
dv dx
or
[f (g(x)]0 = f 0 (g(x)g(x)
A crucial case we will come across a lot is when y = [g(x)]n . In this case,
y 0 = n[g(x)]n
1
g 0 (x)
This is called the general power rule.
Examples:
1. h(x) =
p
2x + 3 = (2x + 3)1/2 . Then
1
h0 (x) = (
1
Functions, Graphs and Limits
1.1
The Cartesian Plane
In this course we will be dealing a lot with the Cartesian plane (also called the xy-plane),
so this section should serve as a review of it and its properties.
y-axis
6
Quadrant 2
Quadrant 1
- x-axis
Cholesky Decomposition
Cholesky decomposition is a special version of LU decomposition tailored to handle symmetric matrices more eciently.
For a symmetric matrix A, by denition, aij = aji . LU decomposition is not ecient enough
for symmetric matrices. Th
Gauss Elimination
Gauss elimination is a way to formalize the eliminate and substitute process we looked at in the
last lecture. As before, it is a two-step process:
Forward elimination eliminate one of the unknowns at a time and continue until the rst so
Cholesky Decomposition Example
Example: Consider the circuit in Figure 1, where R1 = R2 = R3 = R4 = 5 and R5 = R6 =
R7 = R8 = 2. In addition, V1 = V2 = 5. Solve for the loop currents i1 , i2 , i3 and i4 .
Figure 1: Circuit for Example 1
Using Kirchos law,
LU Decomposition
LU decomposition is a better way to implement Gauss elimination, especially for repeated solving a
number of equations with the same left-hand side. That is, for solving the equation Ax = b with different
values of b for the same A.
Note
Error Analysis for Solving a Set of Linear Equations
We noted earlier that the solutions to an equation Ax = b depends signicantly on the matrix
A. In particular, a unique solution to Ax = b exists if and only if A is non-singular. In addition,
in some ca
% ANOVA with Random Effects
% This example shows how to use |anovan| to fit models where a factor's
% levels represent a random selection from a larger (infinite) set of
% possible levels.
%
% In an ordinary ANOVA model, each grouping variable represents
Predictions:
I dont think both of the rectangular prisms will hold the same amount because Container
A is tall and skinny, and Container B is more wider and shorter. I think that Container B
will hold more, because it is wider than Container B so it will
% Generate 10 samples of a Barker code sequence with length 7
% Copyright 2015 The MathWorks, Inc.
hBCode = comm.BarkerCode('SamplesPerFrame', 10);
seq = step(hBCode)
May 12 MATH 112 Total Points: 200
2012 FINAL EXAM
Follow directions carefully:
0 Write your name section number and instructors name on this test and on each of the 6 answer
sheets.
0 Number the answer sheets 1 through 6
0 Do the problems on the answer sh
A
September 26, 2005 MATH 1 laTEST 1 Name:
P2 - 2.3 Section:
Instructions:
Do all problems in the spaces provided. Mark your answers clearly and write them in simplied form. You must show all
appropriate work in order to receive credit for an answer. You
mm MATH 11215373
SECFEGN:
Imitataas:
Do all problems in the spams provided. Mark m answers clearly and write them in simplied mn. You must show all
appropriatc work in order to receive credit for an answer. You may um graphing calculators, but show work
% Apply Array of Gabor Filters to Input Image
%
%
% Read image into the workspace.
% Copyright 2015 The MathWorks, Inc.
I = imread('cameraman.tif');
%
% Create array of Gabor filters, called a _filter bank_. This filter bank
% contains two orientations an
% Calculate Reference Signal Constellation for BPSK Demodulator
% Create BPSK Demodulator System object(TM) and calculate its reference
% constellation.
% Copyright 2015 The MathWorks, Inc.
%
% Create a |comm.BPSKDemodulator| System object.
h = comm.BPSKD
% Adjust Contrast of Grayscale Image Specifying Contrast Limits
%
%
% Read a low-contrast grayscale image into the workspace and display it.
% Copyright 2015 The MathWorks, Inc.
I = imread('pout.tif');
imshow(I);
%
% Adjust the contrast of the image, spec
% Adjust Contrast of RGB Image
%
%
% Read an RGB image into the workspace and display it.
% Copyright 2015 The MathWorks, Inc.
RGB = imread('football.jpg');
imshow(RGB)
%
% Adjust the contrast of the RGB image, specifying contrast limits.
RGB2 = imadjust(