- #1
L Navarro H
- 3
- 0
- Homework Statement
- Find the real functions f so: f' (x) + f (a - x) = e^x
a is a constant
- Relevant Equations
- none
Mod note: Member warned that some effort must be shown.
Last edited by a moderator:
Please post your attempt, per forum rules.L Navarro H said:Homework Statement:: Find the real functions f so: f' (x) + f (a - x) = e^x
a is a constant
Relevant Equations:: none
.
haruspex said:Please post your attempt, per forum rules.
Are you saying that each of those is a solution to the equation? Doesn’t look that way to me. Shouldn't 'a' figure in the answer?L Navarro H said:I use the Abel Identity to find the functions, but I'm no sure if it's correct to used it in this problem
my answer is {e^x , - 1/(3*e^(2x))
A Taylor series expansion is a mathematical tool used to approximate a function using a polynomial. It is based on the idea that any function can be approximated by a polynomial with an infinite number of terms.
A Taylor series expansion is calculated by taking the derivatives of a function at a specific point, usually denoted by "a," and plugging these values into a formula that involves powers of the variable "x." The resulting polynomial is the Taylor series expansion of the function at that point.
Expanding a function using a Taylor series allows us to approximate the value of the function at any point, even if it is not explicitly defined. It also allows us to easily calculate the derivatives of the function at that point.
Expanding a function at a/2 allows us to approximate the function at a point that is closer to the center of the series, which can result in a more accurate approximation. It also allows us to use the properties of even and odd functions to simplify the calculation.
Yes, there are limitations to using a Taylor series expansion. The series may only converge for certain values of x, so it may not be accurate for all values. Additionally, the accuracy of the approximation depends on the number of terms used in the expansion, so it may not be an exact representation of the function.