- Solutions online on “Exercises” page
- Greed question
- Greedy person has x units of something wants ekx more units, want y units means they get cy units
- Think about graphing general behavior of function, and what the axes would represent
- Amount owned grows with time
- Calculus bee problems for review
- Final
- Monday, May 11, noon
- Comprehensive, but emphasizing material since 2nd hour exam
- Designed for 2 hours, you have 3
- Format and rules otherwise similar to hour exams
- Donuts and cider
- SOFIs
- Fill them out via http://go.geneseo.edu/sofi_survey
- Useful to me in improving courses
- Length of parametric curve
- e.g., x = t2/2, y = (2t+1)3/2 / 3, 0 ≤ t ≤ 1
- Connections to Cartesian curves
- y = f(x), put into parametric form
- x = t
- y = f(t)
- Leads to equation for arc length of Cartesian curve
- y = f(x), put into parametric form
- Other applications of integration with parametric curves, some of which work better than with Cartesian curves and some not
- Distance / velocity / acceleration
- Parametrics let you talk about acceleration, etc. in X and Y directions separately
- Introduces notion of “vector” to describe magnitude and direction
- Accelerations can be integrated separately to get X and Y velocities, etc.
- Parametrics let you talk about acceleration, etc. in X and Y directions separately
- Volumes of revolution, areas
- Problems aren’t well defined if curves aren’t functions, often easier to work in Cartesian form
- Surface areas of revolution benefit slightly from ease of talking about arc length
- Distance / velocity / acceleration
- Polar coordinates
- Read section 11.3