# Newton's method - Hewlett Packard

This is a discussion on Newton's method - Hewlett Packard ; I am an AP Calculus teacher with many successful years employing the 48G. Now using the 50G and I would like to know how to put Newton's method in the 50G. It was never a problem on the 48G, but ...

1. ## Newton's method

I am an AP Calculus teacher with many successful years employing the
48G. Now using the 50G and I would like to know how to put Newton's
method in the 50G. It was never a problem on the 48G, but what worked
for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
f'(x) and also define f(x). Enter a numeric value, press N from the
var list and the calc figures out the rest, then you can iterate as
desired. When I do this on the 50, all I get is infinity for the
answer, which apparently means the 50 doesn't recognize f(x) or if it
does, it comes up with zero for its derivative. I don't know much
any help.

Also, anyone else encountered the 50's bizarre treatment of odd
fractional root functions and their graphs? For instance, after many
many failed trials, the only way I have found to get the 50 to draw
the entire graph of y=x^(5/3) is to graph y=x^2/cube root of x! This
is pathetic, and I hope someone knows a much more elegant solution.

Srock

2. ## Re: Newton's method

Since nobody of the experts seems to be online, let me give you a
first hint
in RPN notation, which is the only one I know:
1) store your function to a variable F: e.g. 1-x^2 F STO>
2) calculate the Newton formula and store it to the variable G:
F F X delta / +/- X + G STO>
3) enter a starting value and calculate the next value by:
starting value X STO> G EVAL
and so on

Of course you can do all of these statements within a little program
and hence get an iteration step by pressing one button

Peter

3. ## Re: Newton's method

On Feb 15, 7:30*am, sr...@midland-7.org wrote:
> I am an AP Calculus teacher with many successful years employing the
> 48G. Now using the 50G and I would like to know how to put Newton's
> method in the 50G.

Forgive me for hijacking this discussion, but are you actually using
the HP-50G in the classroom? Do you require your students to have
50Gs also, or do they have a mix of HP and TI calcs?

4. ## Re: Newton's method

On Feb 15, 9:30 am, sr...@midland-7.org wrote:
> I am an AP Calculus teacher with many successful years employing the
> 48G. Now using the 50G and I would like to know how to put Newton's
> method in the 50G. It was never a problem on the 48G, but what worked
> for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
> f'(x) and also define f(x). Enter a numeric value, press N from the
> var list and the calc figures out the rest, then you can iterate as
> desired. When I do this on the 50, all I get is infinity for the
> answer, which apparently means the 50 doesn't recognize f(x) or if it
> does, it comes up with zero for its derivative. I don't know much
> any help.
>
> Also, anyone else encountered the 50's bizarre treatment of odd
> fractional root functions and their graphs? For instance, after many
> many failed trials, the only way I have found to get the 50 to draw
> the entire graph of y=x^(5/3) is to graph y=x^2/cube root of x! This
> is pathetic, and I hope someone knows a much more elegant solution.
>
> Srock

A fractional power is a root of a power. A "root" is an inverse
function. I posted a discussion of the topic in the thread
; the main message is at
If you'll look that over and it's still a problem, please reply to me
offline and I'll be happy to help.
To actually produce your graph, you need to disambiguate the root
(inverse-function) process. There are a total of 3 roots to the
problem. The branch which is positive for positive x transitions to a
complex one if you pass from positive real x to negative real x along
a path which avoids the origin. If instead you graph XROOT(3,x^5) you
will get what you want.
In other words, the CAS underpinnings of the HP50 exhibit what some
might call excessive pedantic fussiness about function definitions but
which others might applaud as deep congruence with the underlying
structure of the complex plane.
Irl

5. ## Re: Newton's method

On Feb 15, 5:30 pm, sr...@midland-7.org wrote:
> I am an AP Calculus teacher with many successful years employing the
> 48G. Now using the 50G and I would like to know how to put Newton's
> method in the 50G. It was never a problem on the 48G, but what worked
> for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
> f'(x) and also define f(x). Enter a numeric value, press N from the
> var list and the calc figures out the rest, then you can iterate as
> desired. When I do this on the 50, all I get is infinity for the
> answer, which apparently means the 50 doesn't recognize f(x) or if it
> does, it comes up with zero for its derivative. I don't know much
> any help.

The problem is that the value of X is being substituted into F(X)
before the derivative is evaluated, which makes the derivative 0. One
way around the problem is to define your Newton function as:

<< -> X << 'X-F(X)/d1F(X)' ->NUM >> >>

-wes

6. ## Re: Newton's method

On Mar 6, 8:53*pm, Irl wrote:
> On Feb 15, 9:30 am, sr...@midland-7.org wrote:
>
>
>
>
>
> > I am an AP Calculus teacher with many successful years employing the
> > 48G. Now using the 50G and I would like to know how to put Newton's
> > method in the 50G. It was never a problem on the 48G, but what worked
> > for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
> > f'(x) and also define f(x). Enter a numeric value, press N from the
> > var list and the calc figures out the rest, then you can iterate as
> > desired. When I do this on the 50, all I get is infinity for the
> > answer, which apparently means the 50 doesn't recognize f(x) or if it
> > does, it comes up with zero for its derivative. I don't know much
> > any help.

>
> > Also, anyone else encountered the 50's bizarre treatment of odd
> > fractional root functions and their graphs? For instance, after many
> > many failed trials, the only way I have found to get the 50 to draw
> > the entire graph of y=x^(5/3) is to graph y=x^2/cube root of x! This
> > is pathetic, and I hope someone knows a much more elegant solution.
> > Again, thanks in advance.

>
> > Srock

>
> A fractional power is a root of a power. A "root" is an inverse
> ; the main message is athttp://groups.google.com/group/comp.sys.hp48/msg/6347e4b8ccb2c203
> If you'll look that over and it's still a problem, please reply to me
> offline and I'll be happy to help.
> To actually produce your graph, you need to disambiguate the root
> (inverse-function) process. There are a total of 3 roots to the
> problem. The branch which is positive for positive x transitions to a
> complex one if you pass from positive real x to negative real x along
> a path which avoids the origin. If instead you graph XROOT(3,x^5) you
> will get what you want.
> In other words, the CAS underpinnings of the HP50 exhibit what some
> might call excessive pedantic fussiness about function definitions but
> which others might applaud as deep congruence with the underlying
> structure of the complex plane.
> Irl- Hide quoted text -
>
> - Show quoted text -

Thanks very much!

7. ## Re: Newton's method

On Mar 7, 11:50*am, Wes wrote:
> On Feb 15, 5:30 pm, sr...@midland-7.org wrote:
>
> > I am an AP Calculus teacher with many successful years employing the
> > 48G. Now using the 50G and I would like to know how to put Newton's
> > method in the 50G. It was never a problem on the 48G, but what worked
> > for the 48 does not work for the 50. On the 48 you define N(x)= x-f(x)/
> > f'(x) and also define f(x). Enter a numeric value, press N from the
> > var list and the calc figures out the rest, then you can iterate as
> > desired. When I do this on the 50, all I get is infinity for the
> > answer, which apparently means the 50 doesn't recognize f(x) or if it
> > does, it comes up with zero for its derivative. I don't know much