Facing problem in analysing Taylor series expansion

Click For Summary
SUMMARY

The discussion centers on the application of Taylor series expansion, specifically regarding the function "sin(x)" and its transformations. Participants clarify that when expanding "sin(x^2)" or "sin(f(x))", one can directly substitute 'x' with "x^2" or "f(x)" in the original Taylor series of "sin(x)". This method is valid and should yield consistent results, as the underlying structure of the series remains intact. Discrepancies in results arise from improper application of the substitution method rather than the method itself.

PREREQUISITES
  • Understanding of Taylor series and its mathematical formulation
  • Familiarity with trigonometric functions, specifically sine
  • Basic knowledge of function composition in calculus
  • Ability to manipulate algebraic expressions and series
NEXT STEPS
  • Study the derivation of Taylor series for various functions
  • Explore the concept of function composition in calculus
  • Learn about the convergence of Taylor series for different functions
  • Investigate common mistakes in applying Taylor series expansions
USEFUL FOR

Students of calculus, mathematicians, and educators looking to deepen their understanding of Taylor series and function transformations.

bibhatsucool
Messages
1
Reaction score
0
This is a very basic question .
Actually in Taylor series expansion of say "sin x" we write the expansion ... (as it is,I am not writing it)
But when we are asked to write the expansion of sin(x^2) we just replace 'x' by "x^2" in the expansion of sin x.
Or if asked some other function such as Sin(f(x)) ,we just replace x by f(x) in Taylor expansion of Sin(x) ...
Instead of finding the expansion of g(x) =Sin(f(x)) term by term mechanically ?why ?
also I found it come out to be different... !
Help guys
 
Physics news on Phys.org
It should not come out differently, if it does you are not doing it correctly. Note that the terms may look different in different sums, but essentially you should always be able to put it on the same form.
 

Similar threads

High School Can We Simplify the Taylor Series Expansion for e^(f(x,y))?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate RIP Edwin F Taylor (1931-2025)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Evaluating Taylor Series at the Mid-Point
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Taylor expansion of an unknown function
  • · Replies 5 ·
Replies
5
Views
3K
Link between Z-transform and Taylor series expansion
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Why does ##u## need to be small to represent the Taylor expansion
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Taylor Expansion Question about this Series
  • · Replies 2 ·
Replies
2
Views
2K
What is the Taylor expansion of x/sin(ax)?
  • · Replies 5 ·
Replies
5
Views
3K
Taylor Series Expansion Confusion
  • · Replies 6 ·
Replies
6
Views
2K
Math terminology in my Taylor Series expansion?
  • · Replies 12 ·
Replies
12
Views
3K