MATH 100 Study Guide - Midterm Guide: Implicit Function, Exponential Growth, Linear Approximation

• School: UBC
• Department: Mathematics
• Course: MATH 100
• Professor: Patrick Walls

Document Summary

Ex: suppose i"m blowing up a balloon. Assume the balloon"s slope is always a perfect sphere. Assume i"m blowing air into the balloon at a rate of 2cm /s. How fast is the radius of the balloon changing, when the radius is. Given: v=volume of balloon, t=time, r=radius of balloon, dv = 1 dt. What to find: dr dt (when r=5cm don"t plug in until after taking the derivative) , a way to relate radius and volume. Take derivative of this equation with respect to t, taking both v and r as functions of t because they"re changing with time. 3 2 dr dt dv = 4 2. (5cm) dr dt dr = 12cm /s3 dt. Identify what you"re trying to find: write down an equation or one or more , solve. In step 1, there should be(at least) three variables. In steps 2 and 3, one of the givens will be a rate(ie: a derivative).