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discussion9 - Math 21A Kouba Discussion Sheet 9 1 Consider...

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Unformatted text preview: . Math 21A Kouba Discussion Sheet 9 1.) Consider function f(x) = (lnfiar4 + 1))5 for a: g —1. Show that f is one—to—one and find its inverse function. 2.) Find all values of K for which the function flat) 2 —2w3 + 3Krr2 is one—to—one. lnzz: 3. . h thtl 2—. )a)S ow a ogBm lnB b.) Assume that 0 < B < l and compute 1.) $1320 logBa: 11.) $138+ logBa: 4.) Compute the following limits. 61-) 11’“ 0‘1)” b.) lim (HEY? c.) lim (“MY/w 12—900 n2 n—>——oo n 1 n sin 3h - 3h , (em —— 1)2 . ' — . ' ——-—— f. l ——-—— d) .332. (1+ n) e) 2.12% m > 1:51 . e—l/w2 . 1 w . . tana: g~> $135 w 11-) .132. (m) 1') 33% (m) m mn(1+m”" k)hm Bn+vfm ”"900 71—)00 d 5.) Find y’ = d—y. Do not simplify your answers. :1: Many ’ . ‘ 2(6) . 3: a: 2 b, 2 (y ) , :m ML 3.) y a; y ) y a: C) y (w+2)m- tan(3m) 132(53 + 1)3(m — 1)5 : . 21y l 2 3_43 (m—2)(x+3)4(2m—5)7 6)“ “my 3” y d-)y +++++++++++++++++++++++++++++++ The following problem is for recreational purposes only. 1 6.) Two bicyclists are twelve miles apart. They begin riding toward each other, one pedaling at 4 mph and the other at 2 mph. At the same time a bumblebee begins flying back and forth between the riders at a constant speed of 10 mph. What is the total distance the bumblebee travels by the time the riders meet ? ...
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