- Calculus Bee
- Today, 4:00 - ?
- Newton 203
- Section 11.2
- Can differentiate parametric equations separately
- Ratio of derivatives is dy/dx
- Calculating length/distance on parametric curves
- L = integral from a to b of square root of sum of squares of derivatives
- L = integral from a to b of square root of sum of squares of derivatives
- Can differentiate parametric equations separately
- Examples
- x = cos(t+π/4), y = sin(t) + 3
- Parametric derivatives give slightly more information about “speed” of particle on curve than dy/dx does
- x = (t+3)3/2 / 3, y = t2 / 4
- Suppose you know equations for horizontal and vertical positions of a rocket:
- Try finding length of a curve from t=0 to t=4
- (Turns out I didn’t find an easily integrable set of functions though)
- (Turns out I didn’t find an easily integrable set of functions though)
- x = cos(t+π/4), y = sin(t) + 3
- More integration and parametric curves