MATH 205 Lecture Notes - Lecture 14: If And Only If, Zdf, Product Rule
In arelated rate problem the idea is to compute
the rate of change of one quantity in terms of the
rate of change of another quantity which may be
more easily measured the procedure is to find
an equation that relates the two quantities and
then use the chain rule to differentiate both sides
with respect to time
Air is being pumped into aspherical balloon so
that its volume increases at arate of 100cm Is
How fast is the radius of the balloon increasing
when the diameter is 50cm
Ig r3
view vand ras afunction of t
volume of asphere
vLH 4g RCH
da the dat Fitr differentiate both sides
431T P
dyed 442 diff now plug in the given data
dir 100
at
fora roar of change of radius IF Io
100 425 dr_ solve for dir
dt dt
IF ants
Aladder 10ft long rests against avertical wall If
the bottom slides away from the wall at arate of
1ftIs how fast is the top sliding away from the
wall when the bottom is 6ft from the wall
gx't y2 to differentiate both
7Key ftp.lx Ttoo
1Tx l2x daxytzydyq os.de for desired
rule
given dx I
at 2GI12ydy 0
dt
goal dy ywhen x6
at to 8
XI 626It 28dy o
dt
z
Car Ais traveling west at 50mi hand car 3is
traveling north at 60mi hBoth are headed for the
intersection of two roads At what rate are the cars
approaching each other when car Ais 0.3 and car B
is 0.4 mi from the intersection
XAX2ty2 zZ
n
Y22xdaff t24 22 days
B
Document Summary
Air rate of 100cm is its that the balloon increasing. How fast when volume increases at a is the radius of the diameter is 50cm. Ig r3 view v and r as a function of t vlh 4g rch da the dat fitr. 100 dyed dir at volume of a sphere differentiate both sides now plug in the given data fora roar of change of radius if i o. If dr_ dt ants solve for dir dt. A ladder 10ft the bottom slides away from the wall at. If rate of is the top sliding away from the long rests against a vertical wall a. 6ft from the wall how fast the bottom is g. 1 tx given dx at goal dy at l. Xi 6 x"t y2 to differentiate both too ftp. lx t. 2 g i 12y dy dt when x 6 to. 2 6 it 2 8 dy o dt z.
