View
281
Download
3
Tags:
Embed Size (px)
DESCRIPTION
Related Rates intro and warmup problems
Citation preview
1
mystarbucks.files.wordpress.com__2008_01_sumoskijumping.jpg
Related Rates
2
In calculus we study the relationship between the ________ of ______________ of variables.
Calculus is the mathematics of ____________,and everything changes with respect to __________.
mystarbucks.files.wordpress.com__2008_01_
sumoskijumping.jpg
mystarbucks
.files.wordpre
ss.com__200
8_01_
sumoskijum
ping.jpg
mystarbucks.files.wordpress.com__2008_01_sumoskijumping.jpg
mystarbucks.files.wordpress.com__2008_01_
sumoskijumping.jpg
mystarbucks
.files.wordpre
ss.com__200
8_01_
sumoskijum
ping.jpg
http://epicaawards.com/assets/epica/2005/finalists/print/images/07070e%20%20%20AirFranceSkiJump.jpg
x = horizontal displacement y = vertical displacement
In algebra we study the relationship between ______________.
Instantaneous rate of change of horizontal displacement with respect totime.
Instantaneous rate of change of vertical displacement with respect totime.
dydt =
http://mathdemos.gcsu.edu/mathdemos/relatedrates/relatedrates.html
dxdt =
changetime
variables
rate change
3
Let V = volume dV/dt = 2gal/min.
Let V = volume dV/dt = 3 cm3/s
Let h = height dh/dt = 30 yd/s
4
x
y
13 m.
Photo by portsmouthmc from Flickr
5
2000
y
θhttp://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/ShuttleAtlantis_launch.jpg
or
6
dV/dt = 5π/3 ≈ 5.2 in3/sA positive value means that the volume is increasing.
dh/dt = 15/π + 1 ≈ 3.8 in3/s.A negative value means that the volume is decreasing.
hr
dr/dt = instantaneous rate of change of radius with respect to time
dh/dt = instantaneous rate of change of height with respect to time
dV/dt = instantaneous rate of change of volume with respect to time
7
Implicit Equations of timeFinding derivatives with respect to time.
8
Quotient Rule Power Rule
9
Related Rates
You are given two quantities
•Both are changing
•They have something to do with each other.
You are asked to find out how their rates of change are related to each otherat some particular instant in time.
On tougher related rate problems, you will need to do some algebrato get from what you know to what you are asked to find.
10