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

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SUMMARY

The Taylor Series Expansion for the function f(x) = (sin x)/x is derived from the series expansion of sin x. The series for sin x is x - x³/3! + x⁵/5! - ..., leading to the conclusion that f(x) = (sin x)/x can be expressed as 1 - x²/3! + x⁴/5! - ... This representation is valid due to the absolute convergence of the series, which ensures the interchange of limits and summation is justified.

PREREQUISITES
  • Understanding of Taylor Series and polynomial expansions
  • Familiarity with the sine function and its series representation
  • Knowledge of absolute convergence in series
  • Basic calculus concepts, including limits and derivatives
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  • Learn about absolute convergence and its implications in series
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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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