Facing problem in analysing Taylor series expansion

AI Thread Summary
The discussion centers on the application of Taylor series expansions, particularly how to derive the expansion for functions like sin(x^2) and sin(f(x)). It highlights the common practice of substituting 'x' with a new variable or function in the existing Taylor series of sin(x) rather than calculating the expansion term by term. Participants emphasize that while the resulting terms may appear different, they should ultimately represent the same function when correctly derived. The confusion arises from the mechanical substitution versus a thorough term-by-term analysis. Proper understanding of Taylor series ensures consistency in results across different forms of the function.
bibhatsucool
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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
 
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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.
 

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