MATH-M 212 Lecture 23: 10.3 Notes (Dec. 9)
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Theorem 10. 7- parametric form of a derivative: if a smooth curve is given by the equations and , then the slope of at is where. 12-9-14 remember is now in terms of o o. Option 2: parametric derivative: equation of tangent line at. Option 2: parametric derivative concave up for all. If and , find the length of the curve for . Ex. o o o o o o o be positive answer turns out negative- if you put , because can be positive or negative, answer will. Given and for , find the surface area when revolved around the -axis and -axis. Given the general cycloid parametric equations and , if , find the length of one arch of the cycloid ( goes from to ). looks similar to. Vectors with calculus: still based on parametrics, position vector: ordered pairs, velocity, acceleration, keeps and separate instead of combined. Gives rates of change in individual and directions: normally,
