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Kouba
Worksheet 41 1. Determine the following limits. a. "m sin 2 e b. "m tan 3 e
9 —>r O 3 e . 650 2 e
C. “m 1~ COS 9 d. “m sin (5 810)
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
x21 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
xv3‘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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 Winter '09
 Kouba
 Calculus

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