3 11 related rates mon nov 10
This presentation is the property of its rightful owner.
Sponsored Links
1 / 13

3.11 Related Rates Mon Nov 10 PowerPoint PPT Presentation


  • 88 Views
  • Uploaded on
  • Presentation posted in: General

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)

Download Presentation

3.11 Related Rates Mon Nov 10

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


3 11 related rates mon nov 10

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


3 11 related rates mon nov 10

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?


3 11 related rates mon nov 10

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?


3 11 related rates mon nov 10

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?


3 11 related rates mon nov 10

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


  • Login