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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.

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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