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Unformatted text preview: Calculus I Exam #1
Spring 2011 Name Show all of your work on this paper in the space provided. Solutions without correct supporting work will not
earn credit. All answers must be exact unless stated otherwise in the problem. Only your best 10 attempts will count towards your grade. © 1. Use the graph of y = f (x) given below to ﬁnd the limits indicated. ~2. a. lim f (x) =
x—>2' b. lim f(x)= i x—)2‘ c. limf(x)= 9M6— x42 2. Use the graph given in #1 t answer.
a. lin31 f (x) = 4 b. xvaiues where the function is not continuous —' 2 3 Q I 3 c. x—values where the function 15 not differentiable. ._ a 1 a I 3 J 5 3.. Evaluate without using a graph or table. Note that possible appropriate answers include
DNE, 00 and  00 a. lim(5 a y)% = i (0 b. lim—SJ—c—+—4:—2 = 9%
A. x40 x j.” 4. Evaluate without using a graph or table. Note that possible appropriate answers include DNE’W'OO f @
a. lim6cot6 =_’i\'— a. lim i=4;
x+1 9—»0 .1r—>1+ ‘m acme __ 9, _
goo Sine rig/“O . e r 9‘5 :: ((3.731— 5. Evaluate without using a graph or table. Note that possible appropriate answers include
DNE, 00 and 00 1 1 (.7. 1'90
a. lim + x __ E 9. ) 1). lim 3x4 _ 5x
x—rO 3 xwo 1' 5x4 :Qizm seam) %'5 >030 axc 21% :"A ,_,i _.___5;
Mam/(ﬂ " 5 6. Evaluate without using a graph or table. Note that possible appropriate answers include
DNE, 00 and 00
2x 1 + x + sin x — 00 b.1im—————
"" H0 3003): a. lim
H 4“ x + 8 7. Find all xvalues where the function is discontinuous. Determine if the discontinuities are removable or nonremovable..
a. f (x) = x _; Discontinuous at x = 5 Reason: " 2 I E
x +
Removable or Nonremovable? Lb b. The deﬁnition of continuity states that a ﬁmction y = f (x) is continuous at a point x = a if and only if
the following three conditions are met: (Make sure you are very precise and use correct notation.) 8. Find f '(x) using the deﬁnition of the derivative: f(x) = 2x2 + x —— 3. Then ﬁnd the equation of the
tangent line to the graph at the point where x = 2. l _ 2  '"(ZJLzi—X'”3
$00.. kg W; .: ' meme?” "312
to two m:$’(2,):q dangle'5 1’7
(2,1) —
\'7:CfX’lg "b ' 9. Find 35 for p = Eli—I {use the deﬁnition of derivative) [q
r ,4  —— F'g
QAWL ( H“) i ’5 M 32 aha/l 23 ‘H
N50 h; ~50 PU : M ( mm m (2 we!)
K50 ‘hCZ%+Zh+D(Z%+I : (923+ ahgeyﬂrﬁjﬁgﬂ‘ “ii
W50 h (Z%+Zh+f)(Zg/~H
I F : likng (2g,+ ZLL—l'l) (23413 10. Sketch the graph of a function that satisﬁes the given conditions. No formulas are required—j ust label the
coordinate axes and sketch an appropriate graph. f(2)=1. f(—1)=o, mama, max)” Jig f(x) = ——00, and lim f(x) = 1 x—v—co 11. a. If um,H1 f(x) = 5 ,must f be deﬁned at x=1? No b. If it is, must f(I) =5? NO
0. Can we conclude anything about the values of f at x=1? Explain your answer. No 5
' t a, SameHm m impaidm
FEW ‘M \chQJAL . ...
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 Spring '11
 PamelaSatterfield

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