espwksht4 - ESP Kouba Worksheet 41 1 Determine the...

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Unformatted text preview: ESP Kouba Worksheet 41 1. Determine the following limits. a. "m sin 2 e b. "m tan 3 e 9 —>r O 3 e . 6-50 2 e C. “m 1~ COS 9 d. “m sin (5 8-10) 6" 0 sin 9 9+6?» 3 e- 6 e. lim tan 8 -1 f lim cos 3 8—1 g. lim 1~cos 2 e h. lim sin (e + h)-— sin e e» o e - hao h sin x for x g 0 2. Sketch the graph of'g(x) = ln ‘5? for O < x < e 2 1 1 + x 2 for x _>_ e 2 x3+1 x2-1 for x¢1,-1 3. Sketch the graph of f(x) = —3/2 for x = -1 3 for x=1 4. Sketch the graph of a function which will satisfy all of the following conditions : a. f(0) = 10 b. f(2) = 0 c lim f(x) = - 00 d lim f(x) = 1 Xar Q'— X—+ 3" e. lim f(x) = 3 f. lim f(x) = + 00 X" 5+ X-> ~ + 5. For each part below, give an example of a function (give a specific formula) f satisfying : a. lim f(x) =+oa = lim f(x) Xq3+ X43" b.‘ lim f(x) =+oo and lim f(x) = — oo x-v3‘L X+3‘ 6 Sketch a ra h for each of the followm #42, M 9 p Q Q‘ i: . a y= 2" b. y: Xz—x X‘1 x2+1 c y=x2'1 d y= |X2”4| x+1 x2—4 e y = x2 f y = x3 x2—9 x2—1 x 9 Y = x2~1 7. Without lifting your pencil, connect the sixteen dots using six straight lines. ...
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