Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# 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