This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ’ Mrs. Waldron BC Calculus § Ch 5.1 (a) (b) (c) (d) (e) (f) (9) Estimating Area with Finite Sums < Ex 1: A bug begins to crawl up a vertical wire at time t = O. The velocity v (in ‘ inches/sec) of the bug at time t/(in seconds), for 0 5 1‘5 8, is given by the function
' whose graph is shown below. —g.__l_..L_;. How far did the bug travel from t = 0 to t = 6?
3+th~ 3 = l; mam What happened exactly at t = 6? M 3+0? Pitd How far did the bug travel from t = 6 to t = 8?
l U161“! dean?) What’s the signiﬁcance of the fact that part of the graph lies above
the xaxis and part lies elow? The P I [4,, a m mpr‘gagt is who kit/«a moves I? .
" " we» U “ " “ \g/
How far did the bug travel from t = 0 to t = 8? ' IO meow
What is the GEOMETRIC or VISUAL significance of this total distance? _
H13 Cl came) down lmcfﬁ Show how the units of time and velocity are put together so that you
end up with the right units for all the HOW FAR questions. d: lthb ‘3, mm,mcw:r mam
' 826;, l. e mm W537 “mam Rectangular Approximation Method (RAM): w 4W Ex 3: A particle starts at x = 0 and moves along the xaxis with velocity v(t) = t2
for time t a 0. Where is the particle at t = 3: N *9 “if” LRAM: MRAM'
01+ *5“ 5+ em (iv = Hairs": C 2.51., gets/I i
: RRAM:
‘ f 2 +12 4' 32"“ /L,‘
Which RAM is the biggest? Smallest? Most accurate?
ﬁchym AREQM 1% 341% xix) 0,33: Oi
m/les+= LEI‘W
ﬁasfacmrw'e’: ”7 KM? g
:5
5.
Z
i,
E
g. .. "vwvmwv'm , Ex 2: Suppose a car is moving with increasing velocity. We measure the car’s velocity every two seconds, and obtain the data in the table below:
Time sec .5 2 4 6 8 10
Veloci ft/sec m 30 38 44 48 50
a) Give a lower and upper estimate for how far the car has gone in the ﬁrst two seconds.
power: 202.0} 3 4/0
upper = a '( Bo ) a 60
b) Give a lower and upper estimate for how _far the7car has gone after 10 seconds. How
much “3:55:23: Isthhmerfeﬂlgrtgosi (signage: E" + 4 ‘4 +44 8.3 3. 5&0
WW”: 2» £313.34" 38 .+ 9‘9; 4,. Li‘g‘t'ﬁiﬁ‘l "'3' H520
Plot the 10second data, and ﬁt it with a smooth curve. Di Rig/anti, =' GO tint: (no) Example 2 continued... Now let’s increase our accuracy and take measurements every second. _2345678910
”i'lIZO 26 30 35 3842 44 464849 50 WW Wmﬁ’ﬁm a) Give a lower and upper estimate for how .far the car has gone after 10 seconds. How
33???? 95'?" gestured + L/ 2. +49 ,.., twe r W .,. W =93
era 2‘; 1:» 30 + 3,5» +32 + clam KM «we 4» WM? MazL/og
(if? D»; gem—ace. = 30 b) If you took measurements every 1/4 second, what would the difference be between
your upper and lower estimates? IS— /
a: = m “Mewsmew“ «WWW c) If you wanted your error to be no more than 1/10th of a foot. how often would you have
to take measurements? ( l
' A _, A n Qn (.9, = Qn (gm x :2 24'“ < 500)
l  _L vh me. = V
6’)“ i 500 ,th ( 2.3 g 226} l ,
Plot the one—second data, and ﬁt it with a smooth curve: (2:; > 8" 27'? : 3—230 Seam v MW : ”mwwwvw—w—v m. \wm«TWW «My
(it/w) WWWWVWWA‘M. WW7, .ww Npmw m, . _ “.mrwsﬂ, Approximate Total Distance Traveled for a s t s b g
E;
E
E:
; m Wm“ “WWW “wavy“ . armr Ex 3: Estimate the volume of a sphere of radius 4. V"? 2%} WW oil 033M 5%
’2f1: VOW <54: 3%le
‘9
7 592 T'I’rz‘ﬁ ) h;
r=oq q
‘QIT/Z'FZ; Wye—v1)
(:0 (=0 [ﬁg/’7 r dWI[le + /5‘+ M/f— ¥j= Mew?” XEQH’; CS};}‘:!‘".,€. DEF/‘7‘ f¥+ 0] = 7°77 ...
View
Full Document
 Spring '10
 Zalla

Click to edit the document details