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Approximation Limits and Derivatives
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2-cycle angle antiderivative approximation Bisection Method Byties calculations complex numbers compute Consider constant converges critical points curve definite integral denote described differential equation direction field endpoint energy equilibrium point 0,0 estimate Euler's Method evaluate exact answer exactly example Exercises Exercise feet per second Find the derivative formula function f(x global minimum height Hence initial conditions initial value problem interval inverse L'Hopital's Rule light ray lim pn limit linear dynamical system linear function logistic models longterm behavior look Mathematica maximum midpoint method mirror negative Newton's Method notation Notice object original particular piece Pn+l Population Year Population positive power series Proof radius radius of convergence real number rectangle region Riemann sum sequence shown in Figure shows side Sketch a graph slope field solution species spring-and-mass system subintervals Suppose tangent Taylor Series Theorem trajectory variable velocity x-axis zero