Download Test 2 with Answer Key - Analytic Geometry and Calculus I | MATH 170 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Math 170-05 Test 2, Spring 2005 Name Key
Test is worth 100 pts. ch 4th
Show all of your work and explain thoroughly where necessary. When in doubt, try
something; you never know what will spark an idea for the solution. I always give partial
credit; so leaving a problem blank is never a good idea. Good luck!
1. (10 pts.) Differentiate the following functions:
a) f(aVe tr = (22) b) A(u) = sin” (cos(x’))
Sty kA 2 E(t) Wa = 2 sinlces (49) d son (cortad
4¢ 3 \(3 24 2x) ® Lonl conta) cu (cos (2) - + cosa?)
= Tn 4x 3K
es alecl Neos late) (- sale) 23
. cain(ecale) ces leaded $s rl : a2)
“ = buh sale Dces (ceolu) £ eau?)
2. (10 pts.) Find = of sin(xy)=x°—y? where y is defined implicitly in terms of x.
ao
i 2 ad
cos (ry) Lng) = 3x87 25
& te
coGy)fx@ey) tse BG
xcosGey) du + gcesday) = Px te fy
( cos Gey) © zy) 2 a 3S = geory)
Od ~ cos lxy) + 24
2
209 ta sine) ~) san (2%) 2
3. (5 pts.) Compute the value of tim 2" C - iw nt c 2
tom gan 2x) 2 sian) iS
«PO 2 2 x
— 5al2x) 2 Lan ends))
=o Tae | oO ae ~
= fe 2h Fe 2) ‘
4. (10 pts.) Using a linear approximation of f(x)=x° at a =2, estimate the value of f(2.01).
Los) = fla\ + £6\ (x-a) Pye 4 20) = 32
@ F(2= SO
Lbe)= 32+ 8OCx-2)
= 32.8
L( 201) = 32 «0(o1) = 324 69 32
se F(rolh * 32.8 gL
5. (15 pts.) A ladder 10 ft tall rests against a vertical wail. If the bottom of the ladder slides
away from the wall at a speed of 2 ft/s, how fast is the angle between the top of the ladder and
the wall changing when the angle is 7/4 rad (= 45 deg)? (Hint: Draw a diagram and let x be the
distance from the bottom of the ladder to the wall. Where is the angle in your diagram? How is it
related to x and the ladder?)
Le @
ql “ an
le
At ote
s™M G: ep a g
hyp fe
, do . to de tf pe
5 aes Ga
Cos © Ge * io ae whe ;
. “ a 4G - es ~ qo
aE Te
Woes & i
ae) = 2. y zz Jz acl
at lea 5 “- wy Ss “s
Ont lo os(F%) fo W244,
