0
How can you determine a mathematical function from a series of ordered pairs?
Wiki User
∙ 14y ago
slope is rise over run. so the change in slope can be determined by the change in Y over the change in X. once you get the slope of the line you can plug a point into the point slope formula (Y-Y1)=m(X-X1). solve for Y to put it into Y=mx+b form.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
What are the applicaton of fourier series?
It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.
Why natural log has base e?
Because when the system of logarithms with the base 'e' was defined and tabulated, it was entitled with the identifying label of "Natural Logarithms". ---------------------------------- My improvement: The natural log base is e (a numerical constant of about 2.718). It is chosen as a log base since there is a mathematical series (a "string" of mathematical numerical terms to be summed) for calculating a logarithm (ie. exponent of the base) of a number, which has a base of e. Series for calculating logarithms with bases other than e have basically not been developed.
What is calculus 1?
Traditionally, and in my learning experiences, calculus is taught in three stages, often referred to as Calculus I, Calculus II, and Calculus III (often shortened to Calc I, Calc II, Calc III). You are asking about Calculus I only, but it is easy to explain all three. Calc I usually covers only derivative calculus, Calc II covers integral calculus and infinite series, and Calc III covers both derivative and integral calculus, but in multiple variables instead of only one independent variable ( xyz = x+y+z as opposed to y = x). This is a traditional collegiate leveling of calculus. This is often changed around in secondary education (in the United States at least). Programs such as AP Calculus often change around this order. AP Calculus AB covers Calc I and introduces Calc II, while AP Calculus BC covers the remainder of Calc II. Now that you know the subject matter, what does it mean? Derivative calculus is a generalized category meant to encompass the computation and application of only derivatives, which are basically rates of change of a mathematical function. A basic mathematical function such as y = x + 2 describes a mathematical relationship: for every additional independent variable "x", a dependent variable "y" will have a value of (x + 2). But, how do you describe how quickly the value of "y" changes for each additional "x"? This is where derivatives come from. The derivative of the function y = x + 2, as you would learn in Calc I, is y' = 1. This means that y changes at a constant rate (called y') of "1" for each additional x. In more familiar terms, this is the slope of this function's graph. However, not all functions have constant slopes. What about a parabola, or any other "curvy" graph? The "slopes" of these graphs would be different for any given value of a dependent variable "x". A function such as y = x2 + 2 would have a derivative, as you would learn in Calc I, of y' = 2x, meaning that the original value of "y" will change at a rate of two times the value of "x" (2x), for each additional increment of "x". You can continue into further derivatives, called second, third, fourth (and so on) derivatives, which are derivatives of derivatives. This is essentially asking "At what rate does a derivative change?". The beginning of Calc I is concerned with introducing what a derivative is, ways to describe the behavior of mathematical functions, and how to compute derivatives. After this introduction is complete, you will begin to apply derivatives to mathematical problems. The description of how derivatives are used to solve these problems is not worth going into, because it would be better for you to connect derivatives to their applications on your own, but you can use derivatives to answer such questions as: What is the maximum/minimum value of a mathematical function on a given interval or on its entire domain? This kind of knowledge can be applied like so: Suppose a mathematical function is found that describes the volume of a box. Knowing that you can use the derivative of this function to find its maximum value, you can then find what value of a certain variable will yield the maximum volume of the box. Another type of application is called a "related rates" problem, in which a known mathematical relationship is used with some given information to describe another property. A question of this type could be: Suppose you have a cylindrical tank of water with a small hole in the bottom, and you measure that the water is flowing out at 2 gallons per minute. At what rate is the height of the water in the tank changing? (This is a simple related rates problem). A full description of integral calculus (Calc II and a basis of Calc III), would take far too long to explain, and it would be easier to explain once you have taken Calc I. Calc III takes the same idea as Calc I and Calc II, but instead of one independent variable "x" changing one dependent variable "y", there are several variables, although in most applications you will only see three, "x", "y", and "z", although the ideas you will learn in the class will apply to potentially infinite variables. The basic ideas of derivatives and integrals will hold here, but the mathematical methods needed and applications possible with multiple variables require additional learning.
What is calculus about?
Calculus is about applying the idea of limits to functions in various ways. For example, the limit of the slope of a curve as the length of the curve approaches zero, or the limit of the area of rectangle as its length goes to zero. Limits are also used in the study of infinite series as in the limit of a function of xas x approaches infinity.
What is the anti-derivative of e-x2?
I believe the questioner means e^(-x^2), which is perhaps the most famous of many functions which do not have anti-derivatives which can be expressed by elementary functions. The definite integral from minus infinity to plus infinity, however, is known: It is sqrt(pi). The antiderivative to e^(-2x) is, (-*e^(-2x)/2) Though the anti-derivative (integral) of many functions cannot be expressed in elementary forms, a variety of functions exist only as solutions to certain "unsolvable" integrals. the equation erf(x), also known as the error function, equals (2/sqrt(pi))*integral e(-t^2) dt from 0 to x. As mentioned before, this cannot be expressed through basic mathematical functions, but it can be expressed as an infinite series. If the question is the antiderivative of e - x2, the answer is e*x - x3/3
Why are there so many mathematical steps required to determine SD?
Because when human mathematicians invented the concept of SD, they defined it as the result of that particular series of mathematical steps. If the steps were fewer or different, the result wouldn't be what they called SD.
What term is defined as a series of ordered groupings of items within a system?
hierarchy
What is exponential series?
I cannot be sure without knowing the context of your question. However, it might be that you are referring to the power series that defines the exponential function. It's difficult to write it down here because there is no provision for writing mathematical formulae. Please see the link.
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
What is the Function of light bulb in an electric circuit?
The function of a light bulb in an electric circuit is that it turns electrical energy into light.
Can electronegativity be factor to determine the activity series of a metal?
There is a possibility that electronegativity can determine the activity series. This activity could knock ions out of solution and ranking in a series.
What has the author Charles Swartz written?
Charles Swartz has written: 'Multiplier convergent series' -- subject(s): Convergence, Multipliers (Mathematical analysis), Arithmetic Series, Orlicz spaces 'Measure, integration and function spaces' -- subject(s): Function spaces, Generalized Integrals, Integrals, Generalized, Measure theory 'Elementary functional analysis' -- subject(s): Functional analysis, Funktionalanalysis
Can every function be expanded in fouriers series?
no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.
What terms is defined as series of ordered groupings of items within a system?
hierarchy
How do you determine whether this series is converging. -1n n2n n0 please show working.?
Unfortunately, the browser used by Answers.com for posting questions is incapable of accepting mathematical symbols. This means that we cannot see the mathematically critical parts of the question. We are, therefore unable to determine what exactly the question is about and so cannot give a proper answer to your question.
What is the function that identifies the data marker for each series in a chart?
The legend is the function that identifies the data marker for each series in a chart.
Can a discontinuous function be developed in a Fourier series?
Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
