Calculus and Analytic Geometry, Volume 1Calculus is the mathematics of motion and change. We can use calculus to find out how rapidly the volume of a metal machine part changes as we cut a slot in it on a lathe. |
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absolute value angle antiderivatives approaches approximation Article asymptote calculate center of mass Chain Rule circle concave constant continuous function coordinates cosine curve defined definition differentiable function distance domain dx/dt dy dx dy/dt ellipse endpoints equal estimate Evaluate EXAMPLE Find dy/dx Find the volume formula function f(x function ƒ gives horizontal hyperbola increases integral l'Hôpital's rule left-hand limits length lim f(x lim h→0 linear local maximum mathematical maximum Mean Value Theorem minimum value negative Newton's method parabola parametric equations plane polynomial positive Problems quadratic quotient radians radius rate of change real numbers rectangle Rolle's Theorem sec²x secant second derivative Show shown in Fig sin²x sinh Sketch slope Solution solve square Suppose surface tangent tion TOOLKIT PROGRAMS triangle velocity vertical x-axis x₁ y-axis y-intercept y₁ zero