**Asymptote:** A line that never touches a graph, it gets infinitely close, but never actually touches the graph

**Euler’s Identity:**

e^{i*π} + 1 = 0

**Conjugate:**

The sign in between the terms is swapped with the opposite

Ex.

3 + 2x = 3 – 2x

3i – 3 = 3i + 3

**Leading Coefficient (1.c):**

The value of the x with the highest power

Ex.

5x^{4} + x^{3} + 6x^{2} + 9x – 10

1.c = 5, because of the five in front of x^{4}

**Extraneous solution (Very important):**

A solution that doesn’t work in the original equation even though you might have gotten it

Ex.^{1}⁄_{x-4}

x = 4

4 – 4 is 0, and you can’t divide by 0, so 4 is an extraneous solution aka one that doesn’t work

## Cool rules of 0

**0 ^{0} = 1:**

1^{1} = | 1 | 0.4^{0.4} = | 0.693 |

0.9^{0.9} = | 0.909 | 0.3^{0.3} = | 0.698 |

0.8^{0.8} = | 0.836 | 0.2^{0.2} = | 0.724 |

0.7^{0.7} = | 0.779 | 0.1^{0.1} = | 0.79 |

0.6^{0.6} = | 0.736 | 0.0001^{0.0001} = | 0.99 |

0.5^{0.5} = | 0.707 | 0^{0} = | 1 |

The further you approach 0 in the exponent that number approaches 1, therefore, it can be presumed that the answer is 1.

**0! = 1:**

Faculty | Answer |

0! | 1 |

1! | 1 |

2! | 2 |

3! | 6 |

4! | 24 |

5! | 120 |

All of the answers get divided by a certain number that counts down by one every time

120/24 = 5

24 / 6 = 4

6 / 2 = 3

2 / 1 = 2

1 / 1 = 1

They count down by 1 all the time so when it comes to 0, 1 divided by 1 is 1

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