## How to enter into Calculator: |

Find f ’(x) |

Enter into calculator, press STO--> & store into x variable. |

Now you can start entering above formula: x - ((f(Xn))/(f ’(x))) |

Then press STO-> & store into the x variable. |

Now press enter, and check result, write it down as answer of X(n+1). |

Continue to do this until you get the exact same result twice. |

## Here is an example: |

f(x)= cos(x) |

You are told to use X |

Find the first derivative of f(x) --> f ’(Xn)= - sin(x). |

Now begin to enter into calculator but entering 0.5 |

Then press STO-> & store into x variable, |

Now you can start entering above formula: x -((cos(x))/(-sin(x))) |

Then press STO--> & store into the x
variable |

Now press enter, and check result, which is 2.33048 something. |

Write this answer down as answer of X(1). |

The first was X0= 0.5 so this answer is X1=2.33048 something |

to whatever significant digit the instructor specifies. |

Now press enter, and check result, which is 1.3806 something. |

Write this answer down as of X(2) = 1.3806 something. |

Now press enter, and check result, which is 1.57312 something. |

Write this answer down as of X(3) = 1.57312 something. |

Now press enter, and check result, which is
1.570796 something. |

Continue to do this until you get the exact same result twice. |

For this equation, you are done with this once you have gotten 1.57079632679 something twice. |

That answer will occur at X(5) and at X(6). |

Here is a link to a page that will do the whole problem

once you enter the original equation and the x value.

http://mss.math.vanderbilt.edu/~pscrooke/MSS/newtonnum.html

**Slant Asymptote:**

Exists ONLY if the degree of N is EXACTLY 1 more than the degree of Q.

* Example: N 4 / Q 3

* N < Q, then y = the x-axis

* N = Q, then y = the Leading Coefficients of N/Q.

* N > Q, then the horizontal asymptote Does Not Exist.

* Set Q(c)=0, Then x = c