MAT 21B Study Guide - Final Guide: Direct Comparison Test, Arc Length, Logarithmic Spiral
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MAT 21B Full Course Notes
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11. 5 - areas and lengths in polar coordinates. = 3: 1 = 3, = " g#r] f. Let f and g be continuous and nonnegative on [, ) If () () on [, ) and () I l converges y y = g(x) y = f(x) a x. I l diverges. y y = f(x) a y = g(x) x. #r "- converges (and its value is less than 1) If 2, ] < so r#g < r#, I converges by the comparison test (with value < r&) 4 1, which is valid if 4. Ex: = 3cos, = 3sin, 0 2. X: = 5cos, = 4sin, 0 2. Ellipse (0, 4) y (-5, 0) x (0, 5) (0, -4: cycloid. = (1 cos) y p (x, y) a t (0, 0) Curve of fastest descent (inverted cycloid: tautochrome - P* q (curve of equal descent: slope of a parametric curve .
