3 11 related rates mon nov 10
Download
Skip this Video
Download Presentation
3.11 Related Rates Mon Nov 10

Loading in 2 Seconds...

play fullscreen
1 / 13

3.11 Related Rates Mon Nov 10 - PowerPoint PPT Presentation


  • 121 Views
  • Uploaded on

3.11 Related Rates Mon Nov 10. Do Now Differentiate implicitly in terms of t 1) 2). Related Rates. When we use implicit differentiation, we obtain dy/dx, or the change of y in terms of x. In many real life situations, each quantity in an equation changes with time (or another variable)

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 3.11 Related Rates Mon Nov 10' - lucius-williamson


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
3 11 related rates mon nov 10
3.11 Related RatesMon Nov 10
  • Do Now
  • Differentiate implicitly in terms of t
  • 1)
  • 2)
related rates
Related Rates
  • When we use implicit differentiation, we obtain dy/dx, or the change of y in terms of x.
  • In many real life situations, each quantity in an equation changes with time (or another variable)
  • In this case, any derivative we find is called a related rate, since each rate in the derivative is related to each other
related rates steps
Related Rates Steps
  • 1) Make a simple sketch, if possible
  • 2) Identify what rate you are looking for
  • 3) Set up an equation relating ALL of the relevant quantities
  • 4) Differentiate both sides of the equation in terms of the variable you want
    • if you want dv/dt, you differentiate in terms of t
  • 5) Substitute in values we know
  • 6) Solve for the remaining rate
slide4
Ex 1
  • A 5-meter ladder leans against a wall. The bottom of the ladder is 1.5 m from the wall at time t=0 and slides away from the wall at a rate of 0.8m/s. Find the velocity of the top of the ladder at time t=1
slide5
Ex 2
  • Water pours into a fish tank at a rate of 0.3 m^3 / min. How fast is the water level rising if the base of the tank is a rectangle of dimensions 2 x 3 meters?
slide6
Ex 3
  • Water pours into a conical tank of height 10 m and radius 4 m at a rate of 6 m^3/min
  • A) At what rate is the water level rising when the level is 5 m high?
  • B) As time passes what happens to the rate at which the water level rises?
slide7
Ex 4
  • A spy uses a telescope to track a rocket launched vertically from a launching pad 6km away. At a certain moment, the angle between the telescope and ground is equal to pi/3 and is changing at a rate of 0.9 radians/min. What is the rocket’s velocity at that moment?
slide8
Ex 5
  • See book
closure
Closure
  • At what rate is the diagonal of a square increasing if its sides are increasing at a rate of 2 cm/s?
  • HW: p.199 #1-37 every other odd
  • Ch 3 Test next week? Mon?
3 11 related rates cont d tues nov 11
3.11 Related Rates Cont’dTues Nov 11
  • Do Now
  • Air is being pumped into a spherical balloon at a rate of 5 cm3/min.  Determine the rate at which the radius of the balloon is increasing when the radius of the balloon is 10 cm.
  • (hint: Volume = 4/3 pi x r^3)
hw review p 199 1 35
HW Review p.199 #1-35
  • Probably all of them
more practice
More practice
  • worksheet
closure1
Closure
  • Hand in: A 15 foot ladder is resting against the wall.  The bottom is initially x feet away from the wall and is being pushed towards the wall at a rate of 0.5 ft/sec.  How fast is the top of the ladder moving up the wall when the bottom of the ladder is 4 feet from the wall?? (Hint: Use Pythagorean Theorem)
  • HW: p.199 #1-35 all other odd
  • p.AP3-1 #1-20, 1-4 due Thurs
  • P.203 #5-11, 17-25, 29-75 85-115 119-123 due Fri
ad