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Calculus 101

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# Calculus 101

Question | Answer |
---|---|

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