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Calculus 101

QuestionAnswer
vertical tangent for Parametric Equations dx/dt = 0 , provided dy/dt does NOT equal 0
second derivative for parametric equations (d^(2)y)/(dx^(2)) = (d/dx)(dy/dx) = ((d/dt)(dy/dx))/(dx/dt)
parametric equation of a circle x = acos(kt)+ c y = asin(kt)+ d
arc length for Parametric Equations L = the integral of the square root of (dx/dt)^2 + (dy/dt)^2 from a to b
derivative of a Parametric Equation dy/dx = (dy/dt)/(dx/dt) , provided dx/dt does NOT equal zero
horizontal tangent for Parametric Equations dy/dt = 0 , provided dx/dt does NOT equal 0
singular point at t for parametric equations dy/dx= (dy/dt)/(dx/dy), provided both dy/dt = 0 and dx/dt = 0 at the same t value
instantaneous speed for parametric equations = the square root of (dx/dt)^(2) + (dy/dt)^2
average speed for parametric equations = (the integral of the quare root of (dx/dt)^(2) + (dy/dt)^(2) on the interval of [a,b]) all divided by the change in t
parametric equation for an ellipse x = acos(kt)+ c y = bsin(kt)+ d
parametric equation for a parabola x = t y = t^(2)
parametric to cartesian 2 ways 1) substitution 2) use Pythagorean trigonometric identity for example cos^(2)(x) + sin^(2)(x) = 1
Created by: felicia.krista