What is the Taylor Series Expansion for f(x) = (sinx)/x?

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The Taylor series expansion for the function f(x) = (sin x)/x can be derived from the series for sin x. The series for sin x is x - x^3/3! + x^5/5! - ..., leading to the conclusion that (sin x)/x simplifies to 1 - x^2/3! + x^4/5! - ... The discussion emphasizes the importance of absolute convergence when justifying this expansion. A rigorous approach may require additional justification depending on the context. Overall, the Taylor series for (sin x)/x provides a useful approximation for small values of x.
jackalsniper
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what is the taylor's series expansion polynomial for the function f(x) = [(sinx)/x]

p/s : i can't open the latex reference, sorry
 
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sin x = x - x^3/3! + x^5/5! -+...
so does it mean that [(sin x) / x] = 1 - x^2/3! + x^4/5! -+ ...?
 
Tha true, but some justification may be requireg depeding the level or rigor you are using.
hint: use absolute convergence
 

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