Unformatted text preview: g ). 6. Consider the curve r = 3 + 2 cos θ . (a) Sketch the curve. (b) Find the area enclosed by the curve. (Express the area as an integral and evaluate it.) 7. Determine if the series is absolutely convergent, conditionally convergent, or divergent. Clearly state any test you use and show that all of the necessary conditions for applying the test are satisﬁed. (a) ∞ X n =2 1 n (ln n ) 2 (b) ∞ X n =2 (11 n )n 8. Consider the power series ∞ X n =1 1 n 2 n ( x3) n . (a) Find the radius of convergence of the power series. (b) Find the interval of convergence of the power series. 9. Let f ( x ) = e x 2 . (a) Write the Maclaurin series for f ( x ). (b) Compute f (10) (0) , the 10 th derivative of f ( x ) evaluated at 0. 10. How many nonzero terms of the Maclaurin series for ln(1 + x ) do you need to estimate ln 1 . 4 to within 0.01? Be sure to justify your solution. 1...
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 Fall '07
 Mikulevicius
 Math, Taylor Series, Mathematical Series, Hyperbolic function, Maclaurin

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