Using Newton's method with the initial point

Using Newton Slide Show:

After running the program newton.bat, press at the initial information screen and then press at the main menu. You can use the following keys to move through the program:

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The other slide shows contained in this program are:

- B. Newton's method applied to the function
**f(x) = sin(x)**using the initial point

**x0 = 11 /32**.

- C. Newton's method applied to the function
**f(x) = sin(x)**using the initial point

**x0 = /2 - 0.02**. If you have several roots then you may not get the root which you expected. - D. Newton's method applied to the function
**f(x) = sin(x)**using the initial point

**x0 = /2**. The tangent line is horizontal and the method fails to find a second estimate for x. - E. Newton's method applied to
**f(x) = x**^{3}- xusing the initial point

**x0 = 1/ pi5**. The method is trapped in a periodic cycle. - F. Newton's method applied to
**f(x) = |x|**using the initial point

**x0 = 1**. Again, the method is trapped in a periodic cycle. - G. Newton's method applied to
**f(x) = x e**^{- x}using the initial point

**x0 = 2**. This time the method fails since the values diverge. - H. Newton's method applied to
**f(x) = x**^{4}- 20 x^{3}- 25 x^{2}+ 500 x + 1using various initial points.