Lecture Notes

Proof of Basic Differentiation Rules

Proof of Differentiation Trigonometric Functions

Lecture Notes

Objectives

Objectives | Model Exercises |
Practice Exercises |
---|---|---|

Find the limit of a function using limit theorems. | ME 1 | PE 1 |

Compute left and right hand limits | ME 2 | PE 2 |

Calculate limits involving infinity | ME 3 | PE 3 |

Find intervals upon which a function is continuous | ME 4 | PE 4 |

Compute limits involving trigonometric functions | ME 5 | PE 5 |

Find the slope of a tangent line using the limit definition of the derivative. | ME 6 | PE 6 |

Determine where a given function is not continuous, not differentiable, or both | ME 7 | PE 7 |

Use the product and quotient rules to find a derivative | ME 8 | PE 8 |

Apply the chain rule to find a derivative | ME 9 | PE 9 |

Find the derivative of a function implicitly | ME 10 | PE 10 |

Use implicit differentiation to solve related rates problems. | ME 11 | PE 11 |

Use the derivative to locate and classify local extrema | ME 12 | PE 12 |

Use the second derivative to determine concavity | ME 13 | PE 13 |

Find the antiderivative of a function | ME 14 | PE 14 |

Use the Fundamental Theorem of Calculus to compute a definite integral | ME 15 | PE 15 |

Use the substitution method of compute a definite integral | ME 16 | PE 16 |

Compute the area between two curves | ME 17 | PE 17 |

Graphing Calculator Tutorials

The Graph of the function |
---|

Limit |

One -side Limits |

Limits at Infinity |

Infinite Limits |

Derivative |

Tangent Lines |

Graph of a Function |

Definite Integral |

Area |

Area Between Curves |