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Taylor Series

The Taylor series is a polynomial of infinite degree used to represent functions like sine, cube roots, and the exponential function. They're how some calculators (and Physicists) make approximations.

Taylor Series - Interval and Radius of Convergence

         

Which of the following represents the interval of convergence of the Taylor series of \(e^x\)?

Find the radius of convergence for the series \(e^{-3x}\).

Find the radius of convergence for the series \(x\sin x\).

Find the radius of convergence for the series \(\sqrt{4 + x}\).

Which of the following represents the interval of convergence of the Taylor series of \(\ln(1-x)\)?

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