Download Resolution for Exam 2 - Analytic Geometry and Calculus I | MATH 170 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Exam 2 Math 170-03 Name.
This exam is worth 100 points. Please show all of your work and explain thoroughly
where necessary. Remember, when in doubt, try something; you never know what
will cause a light buib to be turned on. Plus, I always give partial credit; so leaving a
problem blank is never a good idea. Good luck!
1) (32 points) Calculate the following derivatives
(@) Vxor al Ext — 50 2oetal"
ah .
2 4l3erx nn “03. tx)
(
y. 2 hk
b Ve cial bay"? Se a 1a(r al" 3 “ba (xba) Yuta tA
inven. S s
(b) sinvax 3x - yeos PA
EO? SN
Vxka
(c) -esc@- ad We > — -¢Scecol&
ae > CSC8 CO le
sin’ saints t implify first.
{d) (Icost x)? +307 28) int: try to simplify firs le /
-t bestrbe 6S
2 tb . (243x°-3x) So the “ya Xo
x4 tH Dx ~ (23x -ax {3x"Hsx-2 )
= = [ext tox-2)
1x eae
2. (16 points)The following functions are opine implicitly as a function of x.
(a) Find © if xy! +x yext3y yn Sxy dy dy 4 Uxyt Kady low 3dy
al ax AX ay
So Sd 1 Sy hy yz bony ~y* ¢
ox 50 s - | -dxy~y
Sxytrx*-3
(b) Find » if xtan y= y~1
tony + x sey iG ay =p xSecy ohy ~dy - ~Im y
] OK AX AK AX
=p ody 7 dewy fen y
- —_—s
3x % uC
XSecry ~f Io xSee'y
3. (10 points) If the position of an oscillating particle at time ¢1s given by s(f)=sin 3
find the velocity and the acceleration of the particle at f=7 seconds.
~ thos € a\)\- das FO rhe hn
vity> ses = so Vis)z Se 4 32° 6G Ys
_G
/<2
le
uw
oli
so al MT): -hsn Ts -t
q 3 q
altz ab fi t
35> VR
he same dock at the same time. One travels
4. (10 points) Two boats start moving from tl
ur. At what rate is
dock, south at 20 miles per hour and the other travels east at 15 mile per ho
. -~-the distance between them inereasing.2-hours_later?
{ x leh x he the dita tHe ae Stuveed boat ged
pe HH didhnw the southbourd beat 9¢6.
fot
y lef ot be dine clita betas Hr.
a z
Han 2°: x +y¥ Sb a2 dz = ax de + ay aly
elt off At
Se Az x ax vd \ f : a3
a> aS A ow at 3 hows X= 1f-da +30
At Zz ak z ev yr aoa Yo.
h 22 Vue ta 30"
x eee
Bes ys ou, = figow + a0
= Lasoo
SO.
50
= 32.6 4 4.90
5 3 de, as mph ct thaws,
3 + as fey tae didhnee petwaen Run 13 inceeshy at
Ac MN ofthe hos,
