1. What is the Taylor series generated by a function ƒ(x) at a point x = a? What information do you need about ƒ to construct the series? Give an example.

2. What is a Maclaurin series?

3. Does a Taylor series always converge to its generating function? Explain.

4. What are Taylor polynomials? Of what use are they?

5. What is Taylor’s formula? What does it say about the errors involved in using Taylor polynomials to approximate functions? In particular, what does Taylor’s formula say about the error in a linearization? A quadratic approximation?

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1.  What is the binomial series? On what interval does it converge? How is it used?

2. How can you sometimes use power series to estimate the values of nonelementary definite integrals? To find limits?

3. What are the Taylor series for 1/(1 - x), 1/(1 + x), exp(x), sin x,cos x, ln (1 + x), and arctan x ? How do you estimate the errors involved in replacing these series with their partial sums?