practice(1)

practice(1) - Examples on Related Rates (Section 3.9)...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Examples on Related Rates (Section 3.9) Example 1 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? Guidelines 1. Identify Given information : The rate of increase of the volume of air is 100 cm 3 / s. Unknown : The rate of increase of the radius when the diameter is 50 cm. Draw a diagram . 2. Express these quantities mathematically Let V be the volume of the balloon and let r be its radius. The rate of increase of the volume with respect to time is the derivative dV dt . The rate of increase of the radius is dr dt . 3. Restate the given and the unknown as follows Given dV dt = 100 cm 3 / s. Unknown dr dt when 2 · r = 50 cm. 4. Connect dV dt and dr dt The volume of a sphere: V = 4 3 πr 3 . To use the given information, we differentiate each side of the equation with respect to t (the Chain Rule): 5. Substitute the given information into the resulting equation and solve for the unknown dr dt 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 2 A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

Page1 / 6

practice(1) - Examples on Related Rates (Section 3.9)...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online