Section 2.8 Related Rates Math 1231: Single-Variable Calculus.

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Presentation transcript:

Section 2.8 Related Rates Math 1231: Single-Variable Calculus

Related Rates Problem In a related rates 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 easily measured). Then 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.

Sliding Ladder Problem A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall? How fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall?

Balloon Problem Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm 3 /s. How fast is the radius of the balloon increasing when the diameter is 50 cm?

Problem Solving Strategy

Water Tank Problem A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m 3 /min. How fast is the height of the water increasing?

More Examples