A Taylor polynomial (centered at a) of f(x) can approximate values of f(r) near a. Explain...

  

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A Taylor polynomial (centered at a) of f(x) can approximate values of f(r) near a. Explain why the Taylor polynomial is a better approximation than simply the tangent line of f(x) at a? That is, what qualities does a Taylor polynomial have that the tangent line does not necessarily have? A Taylor polynomial (centered at a) of f(x) can approximate values of f(r) near a. Explain why the Taylor polynomial is a better approximation than simply the tangent line of f(x) at a? That is, what qualities does a Taylor polynomial have that the tangent line does not necessarily have?