CS 342[2019]midterm_solutionsH. MAT 123-01-10-14Midterm Exam 02.12.2019SurnameName InstructorDuration 90 nailiQI. [20pts) Showthat the funtion f (x) = ifSignature100 pointsiscontinuous but notdifferentiable at = O.Since---IS —o,x < if a:= 0 ;y' and Va cues an J --1 many x approaches OQ2. [15 pts] Find the tangent line to the curve In(x2 + !/2) = arcsin(vGS) at the point (0,1).Go-Eksae-s cespecf
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CS 342
[2019]midterm_solutions
H. MAT 123-01-10-14Midterm Exam 02.12.2019
Surname
Name Instructor
Duration 90 naili
QI. [20pts) Showthat the funtion f (x) = if
Signature
100 points
iscontinuous but notdifferentiable at = O.
Since---IS —o,x < if a:= 0 ;y' and
Va cues an J --1 many x approaches O
Q2. [15 pts] Find the tangent line to the curve In(x2 + !/2) = arcsin(vGS) at the point (0,1).
Go-Eksae-s cespecf-6 K
3
2-0 +2-(- and So c.:qu
¯hh.e— -the- U =
Q3. [20ptbl All dimensions Ofa right circular cylinder are changing. When the voulmc is 150cm3, it is increasing at the rate of
5crn3/min and at the same moment, the radius is 5cm and is increasing at the rate of 3cm/min. At what rate the height of the
het h+ is
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Q4. 125ptsl Let f (c) — (a) Find the domain of f. (2ptsl (b) Determine the horizonraJ,vertical and obliqueasymptotes
of f. 15ptsl (c) Find the critical points of f and determine the intervals on which f is increasing and decrcæsing,Find the local
minimum and maximum values. 18ptsl (d) Determine the intervals on which f is concave upward and concave downward, and
find the inflection intso f. 15pt."l(e) Sketch the graph of f.
no Since
Gm 00 1 )
Odue.-
a > 0 showthat the equation + ac —I 0 has EXACTLYONE real solution.
X (rx
Hospi€tkl
2
(. SintQ (eo and a SO) exis4s
a. of O L bU IVT_
-khece- ace- cliffecen+ ceal sobchons ct of
a+iD0 foe) —O) Hhen bU -fhece—eh'sfs Q
c be-4vueeoq such 4ha±
f (c) = gc psi-five and
Which "s a com -fhccfhas exac+& one- real so(u-Ron
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