You missed out one important section:dejet said:Homework Statement
using the Taylor Formula, find the series for the function f(x)=e^{2x}Homework Equations
[tex]\sum \frac{f^{n}(a)}{n!} (x-a)^{n}[/tex]
any help as to where i start would be great. new to series...
Even if you are new to series, you must have some idea of how to start.Homework Help Template said:The Attempt at a Solution
No, that isn't correct. The question states that you must use Taylor's formula, have you tried using it?dejet said:e^2x= 1+2x+ [tex]\frac{2x^{2}}{2!} +\frac{2x^{3}}{3!} +\frac{2x^{4}}{4!}+...[/tex]
there is more to it i think.
dejet said:e^2x= 1+2x+ [tex]\frac{2x^{2}}{2!} +\frac{2x^{3}}{3!} +\frac{2x^{4}}{4!}+...[/tex]
there is more to it i think.
To the OP: Although, substituting 2x for x in the Taylor series for ex as rootX has done is a totally valid (and preferable) method, the question specifically states that Taylor's Formula should be used. Try using it.rootX said:e^x = 1 + x + x^2/2!+ x^3/3! + ...
You substituted 2x for x
so .. x^2 should be (2x)^2 not 2x^2
dejet said:so is this right?
2^(n-1) f(x)=1+2x+4x^2/2!+8x^3/3!+...+2^(n-1)/(n!)...
The Taylor Formula is a mathematical tool used to approximate a function using a polynomial. It helps to find a series of terms that can closely represent the original function.
The Taylor Formula is derived from the Taylor Series, which is an infinite sum of terms that approximates a function at a specific point. The formula is a finite version of the series, making it easier to use for calculations.
To find the series of a function using the Taylor Formula, we need to first choose a point around which we want to approximate the function. Then, we calculate the derivatives of the function at that point. These derivatives are used to create the coefficients of the polynomial, which is the series of the function.
The Taylor Formula allows us to approximate a function with a polynomial, which is often easier to work with in calculations. It also helps us to better understand the behavior of a function around a specific point and can be used to make predictions about the function's values at other points.
Yes, the Taylor Formula can be used for any differentiable function. However, the accuracy of the approximation depends on the smoothness of the function and the chosen point around which the series is calculated. Functions with high derivatives at the chosen point will have a more accurate series.