Sheet5 - Math 210 DHC Kouba Discussion Sheet 5 1 Determine...

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Unformatted text preview: Math 210 DHC Kouba Discussion Sheet 5 1.) Determine the limits of the following sequences. a.) {(1+3/n)”} b.) {3'1“ c.) {M} d.) {2+(—1)n} 571—4 n! e.) {ELSE—ll} f.) {sin(n7r)} g.) {cos(n7r)} h.) {cos(7r/n)} i") {”Sin(”/")} j‘) liminl 1") {i(3+%>2(%)} 12: 1'21 7r/2 7r/4 sec 4) 2.) Convert, but DO NOT EVALUATE, the triple integral / f p3 sin (15 cos ()5 dp dd) d6. 7r/6 0 0 to a.) rectangular coordinates. b.) cylindrical coordinates. 1r 2 sin 9 1'2 3.) Convert, but DO NOT EVALUATE, the triple integral / f f r3 sin 0 cos 6 dz dr d6? 0 0 0 to a.) rectangular coordinates. b.) spherical coordinates. 1 4.) Define the function f (t) = / 8362 d3: . Determine the average value of f over the t interval [0, 1]. 5.) The following equations are given in spherical coordinates. Sketch their graphs in three dimensional space. a.) p21 b.) pzsecd) c.) p=cos¢ d.) p=csc¢ e.) p=csc¢sec6 f.) p=se06 72 1+an 6.) Define a sequence in the following way. Let a1 = 2 and let an.“ 2 for n=1,2,3,4,-~-. a.) Determine a2, a3, and (14. b.) Determine the limit of the sequence. ...
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