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3.11 Related Rates Mon Nov 10

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)

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3.11 Related Rates Mon Nov 10

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  1. 3.11 Related RatesMon Nov 10 • Do Now • Differentiate implicitly in terms of t • 1) • 2)

  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) • In this case, any derivative we find is called a related rate, since each rate in the derivative is related to each other

  3. 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

  4. 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

  5. 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?

  6. 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?

  7. 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?

  8. Ex 5 • See book

  9. 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?

  10. 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)

  11. HW Review p.199 #1-35 • Probably all of them

  12. More practice • worksheet

  13. 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

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