- #1
delsoo
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Homework Statement
for this, my coefficient of x^4 which is 8/4! = 1/3 .. but the ans should be 13/24... can you tell me which part contain mistake?
https://i.imgur.com/05NnrdM.jpg
https://i.imgur.com/28Q9o51.jpg
delsoo said:Homework Statement
for this, my coefficient of x^4 which is 8/4! = 1/3 .. but the ans should be 13/24... can you tell me which part contain mistake?
https://i.imgur.com/05NnrdM.jpg
https://i.imgur.com/28Q9o51.jpg
Homework Equations
The Attempt at a Solution
delsoo said:i redo the question, now my coeffiecient of x becomes only 11 but not 13, now which part is wrong?
https://www.flickr.com/photos/123101228@N03/13809331763/
delsoo said:sorry i really can't find it, i have 2 [ ... ] for d3y/dx3 , and i have 4 [...] for d4y/dx4 , can you be more specifiec telling me which part is wrong? thanks!
Dick said:That's the problem. Yes, you should have four [...]'s for d4y/dx4. In the image you sent, you don't have four. You have three. You are missing one.
A Maclaurin series is a special type of power series expansion that represents a function as an infinite sum of terms. It is named after the Scottish mathematician Colin Maclaurin.
The Maclaurin series of tan (e^x -1) is derived by substituting e^x -1 into the Maclaurin series of tan x and then applying the Maclaurin series for e^x. Simplification and rearrangement of terms results in the final series.
The general formula for the Maclaurin series of tan (e^x -1) is ∑(n=1 to ∞) (-1)^(n+1) (2^(2n) - 1) B_(2n) (x^n) / (2n)! where B_(2n) are the Bernoulli numbers.
The radius of convergence for the Maclaurin series of tan (e^x -1) is infinite, meaning it converges for all values of x. This is due to the fact that the Maclaurin series for tan x has a radius of convergence of π/2, which is larger than the Maclaurin series for e^x.
The Maclaurin series of tan (e^x -1) is used in various areas of mathematics and physics, such as in calculating the solution to differential equations, approximating values of functions, and in the study of harmonic analysis. It is also used in computer science and engineering for numerical analysis and optimization problems.