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Unformatted text preview: Name: ; '20; our; 0N5 Tuesday, 13 September 2005 Instructor: MWF Period: US. Coast Guard Academy Department of Mathematics Calculus I (3111) — Exam 1 This exam consists of eight different pages, including this one. Count the pages
before doing anything else and report any discrepancies to one of the instructors. The exam consists of eleven different problems (some of them with several parts),
with point values as noted, for a total of 100 points. Read each question carefully before answering it. Work alone, in pencil, and show all of your work. Answers without sufficient supporting worker using improper
notation will not receive full credit. Clearly indicate your final answer to each problem by putting 3 around it. The use of books, notes, calculators, crib sheets, etc. is not permitted. Nothing except
pencils and erasers may be brought into the exam room. If you have any questions during the exam, raise your hand but remain seated. One of
the instructors will come to you. Do not leave the exam room without the permission of an instructor. You have a total of 75 minutes to complete the exam. Good Luck! 1. Find all points of intersection of the graphs of the following two functions:
(5 ptS) f(x):x2—2x—6 and g(x):x+4
Xaﬁx—(p = xr‘t‘
=? xix3x /0 = 0
=? (X5)(X+?) = 0
x=5’“2._ for x=5I J=5f¥=7
x=~z jhzﬁzz =? The facinfcs 07c infers: than, are l (5: ‘U and (—212)! 2. Find the equation of the line that passes through the point (1,3) and is perpendicular to the line 2x+3y+5=0. (opts)
XXI3:7 5 '5
4’ 3d : zx '5
= “Ex—é
j 3 a 72..
fmt M9 3=ém + b
9 3,1: b
.. g .5
'7' J gothi, 3. Find the domain and range of the following functions: a. f(x) : 92.x + 3 (4 pts) :9: ZxtS I". 0
ll?"% of [%‘+oo)ls
W 1 b. f(x)=m (5 ptS) :1): 3‘2! '70
'2x >3 X‘% 0: _ (”Do2%.) K : (O)+ao) 4. Sketch the foliowing graphs: (3 pts each)
f(x) = .ln(x) g(x) = ln(x—2)+3 y . y a 6 4 2 I 4 —4 ":2 As —4 —2 r _ .2;
.4
.6 ? x+2 _ .7. (Spts)
J ‘ x+2.. 'ﬁ tyimi the inv’cr‘jc' suited/1 x and j and .50ch JEYJ. 5‘ Given that the function f0“) = is oneto—one, find it’s inverse f‘1(x). 6. Graph and label the inverse function (on the same graph) of the function shown
below: (5 PIS)  .
[JoIre: £0!) :5 sjmmc’cruc Eo {on airt. {ht nnc J: K . Find exact values of the following: 77:
a. [2111— ='
(6) J3 cl. tan(arcsin(—))
WW2.) . 3
c. 3111(arccos(—— . J5 . )) I! = 763 (2 pIS) (2 pm) (4 pts) (4 pts) (4 pIS) 8. Solve the following equation for x: I) 3.\'I = 5 f g, riff = Mai
=)(3xr) QUE 3 #625 :9 3x/ 2 lat—5 Find the followinv 51 .323}— .ﬂx)
b. hrs]. f(x) 6 m for) ‘ENEI
d “3} ﬁx) ‘9 Z! 6. f(5) :: 1+ (9 P15) (2 pLS each) 10. Evaluate the following limits analytically: a. lim (2x2—6x‘l1) = 2 (2)1 g, (2) +1 (5 pts) 142
= . sinm) _ l‘m 5s=ncsx1
C' ll?“ x ) " xeo 5x (5 pts) _ 5' km 632%)
 xbo 5x . 5 5'
2 — = + "" 7:. 2 5
(1. 11—11}( +953) 2. 0+ 1+ co ( pts) x1+4, xi] 11. Consider x) =
f( {2, x 2 1 Is ﬁx) continuous? Justify your answer by using the definition of continuity.
(9 ptS)
j:er‘/ :5 ‘1 FobnomF°J ‘5 tomlr'nuoms “autumn J: 2, £5 qﬂra:dhf ﬁne = comlxnmous {ucvwhcre ...
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