1) The following function, written in pseudocode, inputs INCOME as a variable and outputs the TAX corresponding to that income. You can think of this as a greatly simplified income tax.
1. IF (INCOME
1) For A = cfw_a, b, c and B = cfw_5, 10, 15, 20.
a) How many elements are in A B?
A = 3, B = 4
There are 12 elements in A x B.
b) List the elements of A B.
A x B = cfw_ (a,5), (a,10), (a,15), (a,20)
1
DOE functions for R (version #4)
The file DOE_functions_v4.R contains a collection of R functions that simplify some of the
most common analyses in DOE, and especially in RSM:
Notation
The symbols <
First comments on some things that appeared during the class.
1) Can you have legends on plot? Yes you can, and I added an example in Spectra.r that can
be found in the address given below. I also add
The files that I created today (15.4.2016) can now be found in
http:/users.metropolia.fi/~velimt/Chemometrics/Classes/%234/
Your fourth assignment is to repeat the analyses we did today with the iris
The files that I created today (8.4.2016) can now be found in
http:/users.metropolia.fi/~velimt/Chemometrics/Classes/%233/
Your third assignment is to repeat the modelling of Nt as a function of the N
MTH 1320
9.3 Rates of Change and Derivatives
1/9
For linear functions, we have seen that the slope, m, of the line measures the average rate of change of the function
y2 y1
and can be found from any t
MTH 1320
10.1 Relative Maxima and Minima: Curve Sketching
1/7
Recall: The graph of a quadratic function, f (x) = ax2 + bx + c with a = 0, is a parabola. The graph has a turning
point located at its ve
MTH 1320
10.3 Optimization in Business and Economics
1/6
Denition: Absolute Extrema
The value f (a) is the absolute maximum of f if
for all x in the domain of f (or over
the interval of interest).
T
MTH 1320
10.2 Concavity; Points of Inection
1/5
Denition: Concavity
A curve is said to be concave up on an interval (a, b) if at each point on the interval the curve is
its tangent at the point. If th
MTH 1320
9.5 The Product and Quotient Rules
1/6
In the last section we discussed numerous dierentiation rules. We stated that unlike constant multiples, addition,
and subtraction, dierentiation does n
MTH 1320
9.2 Continuous Functions; Limits at Innity
1/6
In the previous section, we found that if f (x) is a polynomial function, then lim f (x) = f (c) for all values of c. Any
xc
function for which
MTH 1320
12.2 The Power Rule
1/5
Using the only integration technique we have studied (the Powers of x Rule), can we evaluate the following integral?
(4x2 7)3 8x dx
Denition: Dierentials
If y = f (x)
MTH 1320
9.1 Limits
1/9
In various applications we have seen the importance of the slope of a line as a rate of change. We were able to discuss
the slope of linear functions because their slope is con
MTH 1320
9.6 The Chain Rule and the Power Rule
1/7
Thus far we have only investigated how to take a derivative of fairly simple functions like those below.
x2 3
f (x) =
x+1
7
g(x) = 4x5 x3 3x2 + 1
2
MTH 1320
11.1 Derivatives of Logarithmic Functions
Logarithms are concerned with powers (or exponents)!
Recall: Logarithm Basics
The logarithm denition: by = x y = logb x
The logarithmic function y
MTH 1320
9.9 Applications: Marginals and Derivatives
1/5
Revenue and Marginal Revenue
If the demand function for a product is p = f (x) where p denotes the price per unit, then the total revenue
from
MTH 1320
12.1 Indenite Integrals
1/5
So far, we have studied procedures and applications of nding derivatives of a given function. We now turn our
attention to the reverse direction. That is, given a
MTH 1320
11.2 Derivatives of Exponential Functions
Recall: Exponential Functions
The function y = bx is an exponential function with base b, where b > 0 and b = 1.
The natural exponential function y
MTH 1320
9.4 Derivative Formulas
1/6
As one can imagine, nding the derivative of a function via the denition is going to become extremely tiresome.
Luckily, we do not always need to resort to such ted
MTH 1320
9.8 Higher-Order Derivatives
1/4
Because the derivative of a function is itself another function, one might ask how is the derivative changing? To
answer that question, one would just take a
MTH 1320
12.3 Integrals Involving Exponential and Logarithmic Functions
Exponential Formula
If u is a dierentiable function of x, then
In particular,
eu u dx =
ex dx =
Example 1: Evaluate each indenit
12/6/16, 3:40 PM
Comp-XM Exam
Board Query 1
Points: 10
You have answered 1 out of 10
questions. Select your next
question or close the Quiz
when you are done.
2006 Capsim Management Simulations, Inc.
Ashley Gazewood Math 1600 MW 2:30
Cap #2
Problem Statement: How to find the area of various geometric figures, using the same formula Area = Base times Height. Describing how these formulas were deve