Math week of 9/26/16
Math week of 9/26/16 Calculus 1151
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This 1 page Class Notes was uploaded by Brandon Short on Monday October 10, 2016. The Class Notes belongs to Calculus 1151 at Ohio State University taught by Professor Stephen Swihart in Fall 2016. Since its upload, it has received 4 views. For similar materials see Math 1151 - Calculus 1 (11380) in Calculus and Pre Calculus at Ohio State University.
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Date Created: 10/10/16
Calculus notes of 9/26/16 3.11 Related Rates Suppose a spherical weather balloon is filled with gas at a rate of 150 ft /min. What is the rate of change of its radius when the radius is 20 ft? We are given / = 150: Volume increases by 150 ft /min. 3 dt dr We want / whedtr = 20 We need an equation relating V to r. 3 For a sphere, V = 4/3ᴨr dv 2 dr Different Rating time / = 4/3dt* 3r / (implicitdtifferentiation) 2 Or V’ = 4/3ᴨ * 3r r’ Solving for / , dt = dt(4ᴨr ) * /2 dvdt = 1/(4ᴨ * 20 ) * 150 = (3/32ᴨ) ft/min = 0.02984 ft/min Procedure: 1. Identify known rates and desired rates. Label what you already know. 2. Find an equation relating the variables corresponding to known/desired rates, and only these variables. d 3. Take / , rdtembering implicit differentiation. 4. Solve for the desired rate and plug in known values. Warning: Don’t plug in known values until the end.
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