MAT136H1 Study Guide - Final Guide: Conditional Convergence, Integral Test For Convergence, Orthogonal Trajectory
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MAT136H1 Full Course Notes
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Finding arc length formula: solve for [ f "(x) ] 2 plug into s(x) = x 1 [f "(t )]2dt start solve integral. Solving for [ f (x) ] 2 get over same denominator, try to complete the square on numerator. 16 complete the square if denominator already a square/can be left as square, leave denominator (something)2. C is initial population at t = 0. M = carrying capacity equil"m solutions at p = 0 and p = m (no growth!) Hooke"s law : restoring force = - k x k is the spring constant x is length from original. Section 9. 2 direction field: allows visualization of possible graphs short segments of slopes kirchoff"s law: Ri = drop due to resistor (ohms)(amperes) = volts. I = current (amps) equil"m solution: values that satisfy differential eq"n autonomous when independent variable missing from right side e. g. dx/dt = 5k + 3 not dependent on t (time) so all slopes equal horizontally.
