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

# CALCIII Test III

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

Linearization: L(x, y) = | fx(x0 , y0)*(x – x0) + fy(x0 , y0)*(y – y0) + z0 |

Total Differential: df | fx(x0 , y0)dx + fy(x 0 , y 0)dy |

Tangent Line to a Level Curve | f x (x 0 , y 0) (x – x 0) + f y (x 0 , y 0) (y – y 0) = 0 |

Tangent Plane (explicit) | f x (x 0 , y 0) (x – x 0) + f y (x 0 , y 0) (y – y 0) – (z – z 0) = 0 |

Tangent Plane (implicit) | f x (P 0) (x – x 0) + f y (P 0) (y – y 0) + f z (P 0) (z – z 0) = 0 |

Normal Line | x = f x (x 0 , y 0) t + x 0 , y = f y (x 0 , y 0) t + y 0 , z = - t + z 0 |

f has a local max at (a, b) if f xx < 0 and | f xx f yy - f xy 2 > 0 at (a, b) |

f has a local min at (a, b) if f xx > 0 and | f xx f yy - f xy 2 > 0 at (a, b) |

f has a saddle at (a,b) if | f xx f yy - f xy 2 < 0 at (a, b) |

inconclusive if f xx f yy - f xy 2 | = 0 at (a, b) |

(r, θ, z) → (x, y, z) | x = r cos θ, y = r sin θ, z = z |

(x, y, z) → (r, θ, z) | r = sqrt(x^2 + y^2), tan θ = y/x, z = z |

(ρ, θ, Φ) → (r, θ, z) | r = ρ sin Φ, θ = θ, z = ρ cos Φ |

(r, θ, z) → (ρ, θ, Φ) | r = sqrt(x^2 + y^2), tan θ = y/x, z = z |

Created by:
timmay23