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Disc10 - Math 21B Kouba Discussion Sheet 10 1 1 Consider...

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Unformatted text preview: Math 21B Kouba Discussion Sheet 10 . 1 1.) Consider the region R lying below the graph of y = — and above the x—axis on the interval x [1,00) . a.) Determine if R has finite or infinite area. b.) Form a solid by revolving R about the x—axis. Determine if the resulting volume is finite or infinite. c.) Form a solid by revolving R about the y-axis. Determine if the resulting volume is finite or infinite. 2.) Compute the following imprOper integrals. oo 1 0 3m 00 1 1 00 \/§ 1 82+]. 7 e 2 d.) —oox2+9 d1: e.)/1 13-1 do: f.)/0 a: lnzc dx °° 1 5 1 °° 24 . h. __ 3 ________ g) ./2 SCUM? d2: ) [0 «25—952 do: I) /1 2$2+5m+2 d9” 5 8:6 00 3 7r/2 j.) / dm k.) / 1:26z d1: 1.) / cscxcotzz: d3: 0 $2 ‘ 9 — o 00 oo oo 1 1 00 6—1/2.- m.) / ace—5”” da: n.) / —2 dac o.) / Ina: da: p.) / 2 d1: 0 o a: o 0 13 3.) Use the Comparison Test to show that the following improper integral converges, i.e., is co 1 -—————- dx /1 Vm3+16 4.) Use the Comparison Test to show that the following improper integral diverges, i.e., is °° a: + 4 —-——— d1: 1 V$3+16 5.) Find the slope of the line tangent to each graph at the given value of 6. finite : infinite : a.) r=2+cost9 for 0:37r/4 b.) r=4sin0 for 0:7r/3 c.) r=9+1 for 0:71" 6.) Find the area of the region bounded by the graphs of 0 : 1r/ 6 , 6 = 7r /4 , and r = sec 0 . 7.) Find the area of the region lying inside the graph of 'r = 2 + sinl‘} and outside the graph of r = c056 . 8.) Find the area of the region shared by the circles r = x/gsinél and 7‘ = 0059 . 9.) Find the area of the region lying inside the graph of 7' = 4sin0 and above the line 7‘ = 0800 . “Deal with the faults of others as gently as with your own.”— Chinese Proverb ...
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