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# Taylor Series

### Its for a calc project

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

e^x | 1+x+(x^2)/2!+(x^3)/3!+(x^4)/4!+...+(x^n)/n!+(e^Zn)(x)^(n+1)/(n+1)! |

ln (1+x) | x-(x^2)/(2)+(x^3)/(3)-(x^4)/(4)+(x^5)/(5)+...... |

1/(1+x) | 1-x+(x^2)-(x^3)+(x^4)-(x^5)+..... |

1/(1-x) | 1+x+(x^2)+(x^3)+(x^4)+(x^5)+..... |

sin(x) | x-(x^3)/3!+(x^5)/5!-(x^7)/7!+(x^9)/9!+......+term in x^n+[+/-sin(Zn) or +/-cos(Zn)](x)^(n+1)/(n+1)! |

cos(x) | 1-(x^2)/(2!) +(x^4)/(4!)-(x^6)/(6!)+....+term in x^n+[+/-sin(Zn) or +/-cos(Zn)](x)^(n+1)/(n+1)! |

tan^-1 (x) | x-(x^3)/3 + (x^5)/5 -... (-1)^n (x^2n+1)/2n+1+... |

e^x (general form) | Σ(x^n)/ (n!) n=0 to infinity |

ln (1+x)(general form) | Σ(-1)^n-1 (x^n)/n n=1 to infinity |

1/(1+x) (general form) | Σ(-1)^n x^n , for |x| < 1 n=0 to infinity |

1/(1-x) (general form) | Σx^n,for |x| < 1 n=0 to infinity |

sin(x) (general form) | Σ(-1)^n x^2n+1/(2n+1)! , for all real x n=0 to infinity |

cos(x) (general form) | Σ(-1)^n x^2n/(2n)! , for all real x n=0 to infinity |

tan^-1 (x) (general form) | Σ(-1)^n x^2n+1/(2n+1) , for |x| < 1 n=0 to infinity |

Created by:
kukuriikuu