This is a sample, and is meant to represent the material usually covered in Math 9C for the final. An actual test may or may not be similar.
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Test if the following sequences converge or diverge. Also find the limit of each convergent sequence.
For each of the following series, find the sum if it converges. If it diverges, explain why.
Determine if the following series converges or diverges. Please give your reason(s).
(a) Find the radius of convergence for the power series
(b) Find the interval of convergence of the above series.
Find the Taylor Polynomials of order 0, 1, 2, 3 generated by at
(a) Express the indefinite integral as a power series.
(b) Express the definite integral as a number series.
(a) Consider the function Find the first three terms of its Binomial Series.
(b) Find its radius of convergence.
Find such that the Maclaurin polynomial of degree of approximates within 0.0001 of the actual value.
A curve is given in polar coordinates by
(a) Sketch the curve.
Find the length of the curve given by