Mathematics Cheat Sheet: Derivatives, Vectors, Probability, and More
Derivative Table
f (x) = K f ‘(x) = 0
f (x) = x f ‘(x) = 1
f (x) = kx f ‘(x) = k
f (x) = kx + b f ‘(x) = k
f (x) = xn f ‘(x) = nxn-1
f (x) = u (x) + v (x) f ‘(x) = u’ (x) + v ‘(x)
f (x) = u (x) * v (x) f ‘(x) = u (x) * v’ (x) + v (x) * v ‘(x)
f (x) = u (x) / v (x) f ‘(x) = [v (x) * u’ (x) – u (x) * v ‘(x)] / [v (x)]2
f (x) = [u (x)]n f ‘(x) = n[u (x)]n-1 * u’ (x)
f (x) = sin x f ‘(x) = cos x
f (x) = sin [u (x)] f ‘(x) = cos u * u’
f (x) = cos x f ‘(x) = – sin x
f (x) = cos
Understanding Dimensional Metrology and Tolerances in Manufacturing
Dimensional Metrology and Tolerances
Precision and Range
When a set of readings of a measurement has a wide range, it indicates low precision. The difference between the lower and higher values that an instrument is able to measure is called range.
Uncertainty Factors
When determining the uncertainty for a particular measurement device, the common uncertainty factors that should be included are: technician’s error, errors in the measurement technique and method, and random variability of the measurement
Read MoreEducational Group Meeting Minutes: Children 5 Years
Ministry of Education, Culture and Sports
CEIP “El Puerto” C / Canarias, 6 Tél: 922-481089 / Fax: 922-480857 38010451@gobiernodecanarias.org
TEAM MEETING MINUTES OF EDUCATIONAL GROUP: CHILDREN-5 YEARS
Meeting Coordinator: Abel Hernandez Rosa Property
DATE: 11-12-2008 TIME: 16:00 LOCATION: Center Library
| Name | Position / Specialty | SIGNATURE |
|---|---|---|
| Abel Hernandez Rosa | Real Tutor | |
| María del Cristo Medina Calero | Religion | |
| Elisa Gomez Pulido | Psychomotricity | |
| Maria Reyes Rodriguez Cabrera | English |
AGENDA
- Evaluation of the 1st Quarter
- Difficulties
Understanding Investment Concepts: Expected Returns, Minimum Variance Portfolios, and Utility
1. Below is given the log returns of asset X for 4 years. The standard deviation of the log returns is 5.39 %. Calculate the expected return of the asset (this means the arithmetic mean of the asset)- 1.15% 0.91% -0.04% 3.65% 1.77% 1.80% 3.36% -1.96% -0.12% -0.12% 3.50% 0.09% Step1- Calculate the average in this case = 0.0115,0.0091,(0.0004),0.0365,0.0177,0.0180,0.0336,(0.0196),(0.0012),(0.0012) ,0.0350,0.0009 add all and divide by 12 which = 0.0117 then + ½ (( 0.0539 )^2) = 0.0131 then convert
Read MoreAlgebra Cheat Sheet: Solving Linear & Quadratic Equations
Section 1
Chapter 1: Solving Linear Equations Cheat Sheet
Objective 1: Solve a Linear Equation
Concepts and Rules:
- A linear equation is in the form of ax + b = c, where a, b, and c are real numbers.
- The goal is to isolate the variable (x) on one side of the equation.
- Balancing: Perform the same operation on both sides to maintain equality.
Step-by-Step Solving Process:
- Start with the equation in the form ax + b = c.
- Use inverse operations to isolate x:
- To remove/add a constant (b): Perform the opposite operation
Multiple Regression Analysis in Estimating Annual Salary
Multiple Regression Analysis
Multiple regression analysis is an extension of simple regression analysis. It uses two or more independent variables to estimate the value of a dependent variable. This method identifies the best-fitting line based on the method of least squares.
Additional Concepts
- Constant (b0 intercept): The value of the dependent variable (DV) in the regression equation when all independent variables (IVs) are equal to 0.
- Partial Regression Coefficient (conditional coefficient): Shows