Zero | Homework Help

Posts Tagged ‘zero’

Horizontal Asymptotes

Tuesday, September 29th, 2009

How to Find Horizontal Asymptotes

Description

A detailed tutorial on how to find horizontal asymptotes. Step by step tutorial including several examples of how to find horizontal asymptotes for reference.

Overview

There are several different types of asymptotes. In this tutorial, we will be discussing horizontal asymptotes. In order to find the horizontal asymptotes of a function, take the limit of the function to infinity. Every function has a horizontal asymptote if it has a limit to infinity. The limit is your horizontal asymptote.

Tags: algebra, asymptotes, closer, curves, distance, farther, horizontal, infinity, limit, linear, lines, Math, negative, nonlinear, oblique, origin, postive, straight, vertical, zero
Posted in Algebra | No Comments »

Vertical Asymptotes

Tuesday, September 29th, 2009

How to Find Vertical Asymptotes

Description

A detailed tutorial on how to find vertical asymptotes. Step by step tutorial including several examples of how to find vertical asymptotes for reference.

Overview

There are several different types of asymptotes. In this tutorial, we will be discussing vertical asymptotes. In order to find the vertical asymptotes of a function, we must first determine if there is a vertical asymptote. There is only a vertical asymptote if the limit of the function is equal to positive or negative infinity. If that is true, then the limit will reveal the vertical asymptote.

Asymptotes

Tuesday, September 29th, 2009

Introduction to Asymptotes

Description

A detailed tutorial on how to find asymptotes. Step by step tutorial including several examples of how to find asymptotes for reference.

Overview

An asymptote of a curve is a way of describing the behavior of the curve above the origin by comparing it to another curve. The second curve is considered an asymptote of the first if the distance between the two approaches zero as the points themselves extend to infinity. Another way of describing this is that the first curve gets closer to the second as it gets farther from the origin. If the asymptote is a straight line, it is called a linear asymptote.

Tags: algebra, asymptotes, closer, curves, distance, farther, horizontal, linear, lines, Math, nonlinear, oblique, origin, straight, vertical, zero
Posted in Algebra | No Comments »

Maclaurin Series

Thursday, September 24th, 2009

How to Solve the Maclaurin Series

Description

A detailed tutorial on the solving of a Maclaurin series. Step by step tutorial including several examples of how to solve a Maclaurin series for reference.

Overview

A Maclaurin series is a Taylor series that is centered at zero instead of one of the other numbers. A Taylor series is a representation of a function as an infinite sum calculated from the values of its derivatives at a single point. A Maclaurin series can be expressed like this:

$f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots$

The only difference is that a Maclaurin series will be centered at the point zero. Many Maclaurin series, specifically e to the x, can easily be memorized so solving by a chart would not be necessary.

Tags: Calculus, chart, derivatives, factorial, function, infinite sum, Maclaurin series, Math, point, Taylor series, value, zero
Posted in Calculus | No Comments »

Taylor Series

Thursday, September 24th, 2009

How to Solve the Taylor Series

Description

A detailed tutorial on the solving of a Taylor series. Step by step tutorial including several examples of how to solve a Taylor series for reference.

Overview

A Taylor series is a representation of a function as an infinite sum calculated from the values of its derivatives at a single point. If the series is centered at zero, then it is called a Maclaurin series, even though it is still a Taylor series. A Taylor series can be expressed as

$f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots$

A more compact form of which is $\sum_{n=0} ^ {\infin } \frac {f^{(n)}(a)}{n!} \, (x-a)^{n}$

A popular way to solve a Taylor series is by using a chart to calculate all possible derivatives and set into their proper equations.

Tags: Calculus, chart, derivatives, factorial, function, infinite sum, Maclaurin series, Math, point, Taylor series, value, zero
Posted in Calculus | No Comments »

Rolle’s Theorem

Thursday, September 24th, 2009

An Overview of Rolle’s Theorem

Description

A detailed tutorial on how to solve problems using Rolle’s Theorem. Step by step tutorial including examples of how to solve problems using Rolle’s Theorem for reference.

Overview

Rolle’s Theorem is a special instance of the Mean Value Theorem, and can be used to prove the Mean Value Theorem. Rolle’s Theorem states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero. Mathematically this can be expressed as if a real-valued function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists a c in the open interval (a, b) such that f ‘(c) = 0.

Tags: Calculus, closed, continuous, differentiable, function, graph, interval, Math, mean value theorem, open, real-valued function, rolle's theorem, slope, tangent line, zero
Posted in Calculus | No Comments »

The Number Zero

Thursday, September 24th, 2009

The History of the Number Zero

Description

A detailed tutorial on the history of the number zero. Step by step tutorial including several citations of the history of the number zero for reference.

Overview

Zero is a number we’ve heard about a lot. It’s not a counting number, it’s not negative or positive, it’s not even or odd. It’s not a prime number, it doesn’t even really fit the definitions of a real number or a whole number although it is considered to be both. It is certainly one of the most interesting numbers you can work with. In writing, 0 is distinguished from the capital letter O by either being a bit smaller or having a bit more of an oval shape. Often when handwriting as opposed to typing a line will be drawn through the zero, although this can be confused with an empty set if you are learning set theory. The name zero came from several different lanuages, in which words similar to zero translated to “is empty” “nothing”, and “void”. When doing calculations you must be sure to know the difference between 0 and NaN – “not a number”. Often things that look like they should be zero (0 / 0, for example) are really not numbers at all.

Tags: 0, arithmetic, empty, even, Math, NaN, negative, nil, not a number, nothing, nought, null, number, odd, oh, positive, prime, real, void, whole, zero
Posted in Arithmetic | No Comments »

Maxwell’s Equations

Tuesday, September 22nd, 2009

How to Solve Maxwell’s Equations

Description

A detailed tutorial on the solving of Maxwell’s Equations. Step by step tutorial including several examples of how to solve Maxwell’s Equations for reference.

Overview

Maxwell’s equations are a set of four partial differential equations that describe the properties of electric and magnetic fields and relate them to their sources, charge density and current density. The result of these equations is that they show light is an electromagnetic wave. The four different equations and the way to express them is as follows:

Gauss’s Law: relates electric charge contained within a closed surface to the surrounding electrical field.

Differentiation: $\nabla \cdot \mathbf{D} = \rho_f$

Integration: $\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\;\cdot\mathrm{d}\mathbf A = Q_{f}(V)$

Gauss’s Law for Magnetism: states that the total magnetic flux through a closed surface is zero.

Differentiation: $\nabla \cdot \mathbf{B} = 0$

Integration: $\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf B\;\cdot\mathrm{d}\mathbf A = 0$

Maxwell-Faraday Equation: describes how a changing magnetic field can create an electric field.

Differentiation: $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$

Integration: $\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l}� = - \frac {\partial \Phi_{B,S}}{\partial t}$

Ampere’s Circuital Law: states that magnetic fields can be generated by electrical current and changing electric fields.

Differentiation: $\nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t}$

Integration: $\oint_{\partial S} \mathbf{H} \cdot \mathrm{d}\mathbf{l} = I_{f,S} + \frac {\partial \Phi_{D,S}}{\partial t}$

Tags: Ampere's Circuital Law, change density, closed surface, current density, density, electric charge, electric fields, electrical current, electromagnetic wave, Gauss's Law, Gauss's Law for Magnetism, Guassian surface, light, magnetic field, magnetic flux, Maxwell's equations, Maxwell-Faraday Equation, Physics, Science, zero
Posted in Differential Equations | No Comments »

Monotonicity Theorem

Thursday, September 17th, 2009

Explanation of the Monotonicity Theorem

Description

A detailed tutorial on the solving of the Monotonicity Theorem. Step by step tutorial including several examples of how to solve the Monotonicity Theorem for reference.

Overview

The Monotonicity Theorem is used to determine if a function is increasing or decreasing. The Monotonicity Theoream states that:

If f ‘(x) > 0 the function is increasing

If f ‘(x) < 0 the function is decreasing

This is basically a repeat of information you already know. The derivative is the same as the slope of a line, and it is obvious to anyone who has spent time studying grpahs that a positive slope increases and a negative slope descreases. Simply find your function, take a derivative, and set it to either less than or greater than 0 to figure out if your graph will be increasing or decreasing.

Tags: 0, Calculus, decreasing, derivative, function, greater than, increasing, less than, Math, monotonicity, monotonicity theorem, slope, zero
Posted in Calculus | No Comments »

l’Hôpital’s Rule

Friday, September 4th, 2009

An Overview of l’Hôpital’s Rule

Description

This video explains how to properly use l’Hôpital’s Rule and tells us why it is sometimes necessary to use l’Hôpital’s Rule instead of another method of finding the limit. This video also gives several example problems of how to use l’Hôpital’s Rule.

Overview

l’Hôpital’s Rule is a rule of calculus that helps when evaluating the limit to infinity. l’Hôpital’s Rule states that:

d/dx [f(x) / g(x)] = d/dx [f\'(x) / g\'(x)]

In other words, l’Hôpital’s Rule says that when you need to find the limit of a division equation, you may find the derivative of the numerator and denominator seperately and place them into your equation. Do not use the quotient rule to find an overall derivative or this will not work.

Tags: Calculus, derivatives, division, infinity, l'Hôpital, l'Hôpital's Rule, limit, limit to infinity, Math, zero
Posted in Calculus | No Comments »