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Math 131 Name:
Spring 2010 Name-nu:
Midterm 1
Form B Lecturer:
Rec. Instructor:
Rec. Time:
Instructions:
¢ You have 48 minutes to complete this exam. It consists of 8 problems on 9 pages including
this cover sheet and is ‘worth @ total of 100 points. The value of each question is listed below.
e You may not use any books or notes during this.exam.
e Calculators are permitted EXCEPT those calculators that have symbolic algebra or calculus
capabilities. In particular, the following calculators:and their upgrades are not permitted: TI-89,
’ T1-92, and HP-49. In addition, neither PDAs, laptops nor cell phones are permitted.
© Make sure to read each question carefully.
* Please write clearly and make sure to justify your answers. Correct answers with no
supporting work may receive no. credit.
« Please write-your answers on the indicated lines.
e A random sample of graded exams will be xeroxed before being returned.
Problem | Point Value | Score
1 12
2 12
3 12
4 10
5 12
6 12
7 16
8 14
Total 100
(1.) Find the following limits:
_ +.10e-+24 >
(a) 2m, at+4 ~
= len Gert ioute
ee
XO
= lon EG
2a? 4+ lis +12 +00
(b.) Im “Dogo :
a ln Gur 3 ra)
xeat “(4 xg ) ~ FOP
(3.) Given
a? — 144
iT ife <0
fey-d 12 ife=0
= — a ifx>0
Find the following:
(a) lim f(2)= 12
(b.) lim, f(@) = _12
(e.) lim f(a) =_DNE
(d.) Is f(x) continuous at z = 0? Why? No, becauge ks 4x DNE.
(e.) Find all points of discontinuity for f(z) X20, (2, -'2
@) tim fa)-_ 2S
(4.) Solve the given inequality using a sign graph:
4c? + 17a+4
2a3 >0
(4x 41x44)
XS
7O
Answer (4.): t 4, “k Juls, ox) :
(5.) Find the equation of the tangent line to the graph of the function f(z) = 7a — 3523 + 142? at
c=1,
floc) 2827— 105x748
lope = L1y = 28 ~ (06428 =~ 49,
We §() = F-3S4id = {4
Couction st Y— C14) = -49 (x~1)
4= 749 -1)~ 14
Answer (5.): y = ~49lep-l4 |
(6.} Use definition of the derivative given below to find f’(z) where f(z) = 1
44+5a°
1") = lig fe+ M) - f@
—_ _-bL.
= [im Atetaty ~ Avsx
ho la
z by Geisn) — (Ae soer))
Wo lh (Aes txth)) (4 Sox)
a lm SSK
Leo K (44Slotn)) (44x)
z= ~§
(446%
eee
Answer (6.): f!(z) =
7
