MAC 2312 Midterm: MAC 2312 FIU Exam f13k
15 Feb 2019
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Prof. s. hudson: [10 pts] classify each series as d for divergent, ca for absolutely convergent, or cc for conditionally convergent. Justify your answers with convergence tests and calculations. P+ k=2( 1 ln k )k: [10 pts] state and prove the integration formula for area in polar coordinates. Draw a picture showing , , etc. , and use a p and a limit in your explanation: [approx 10 pts] find the mcl. series for f (x) = 1 + 3x. Shells are suggested, but other methods are ok. for 2 extra points, compute the integral: [10 pts] use the usual series for ex to approximate e to four decimal-place accuracy (to within . 00005). You can leave your answer as a sum (don"t simplify it). Use the rn formula to nd the smallest allowable n. [hints: 6!=720, 7!=5040, 8!=40320 9!=362,880 and e < 3]: [20 pts] answer true or false:
