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trigkid213


Member


Joined: 30 Mar 2006
Posts: 208

Posted: 23 Sep 2006 05:51:12 pm    Post subject:

This is just a general 89 question, but we just learned implicit differentiation in calculus and I wanted to know if there is a way to do it on the calculator. Also, what about graphing?
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Fallen Ghost


Elite


Joined: 15 Jun 2006
Posts: 955

Posted: 23 Sep 2006 06:25:50 pm    Post subject:

Shouldn't this be in Basic forum?
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DarkerLine
ceci n'est pas une |


Super Elite (Last Title)


Joined: 04 Nov 2003
Posts: 8328

Posted: 23 Sep 2006 06:34:46 pm    Post subject:

Yes, it should.

I believe you use an undefined function in terms of the variable with respect to which you're differentiating. Example:

We want to differentiate x2+y2=1.

We write this as [font="courier new;font-size:9pt;line-height:100%;color:darkblue"]d(x2+y(x)2=1,x)
.

We get an equation in terms of y, dy/dx, and x. If that's all you need, great. If not, we edit the equation and replace [font="courier new;font-size:9pt;line-height:100%;color:darkblue"]d(y(x),x) with another variable such as [font="courier new;font-size:9pt;line-height:100%;color:darkblue"]dydx. Then we [font="courier new;font-size:9pt;line-height:100%;color:darkblue"]solve(2*y(x)*dydx+2*x=0,dydx) to get our final answer, dy/dx = -x/y.

For some reason, this also returned the warning "may return false equation" when I tested it. So make sure to check your answers.

Last edited by Guest on 22 Dec 2006 12:23:00 pm; edited 1 time in total
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trigkid213


Member


Joined: 30 Mar 2006
Posts: 208

Posted: 23 Sep 2006 07:00:20 pm    Post subject:

Thanks.

[EDIT]
I wrote a program to do implicit differentiation and I wanted to know if it's possible to display an answer on the home screen instead of the I/O screen (I know 84 BASIC but I'm not very familiar with 89). Also, is it possible to graph a function like yx^2+y^2=2x without solving for y?


Last edited by Guest on 23 Sep 2006 08:33:47 pm; edited 1 time in total
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v0dKA


Newbie


Joined: 04 Mar 2006
Posts: 11

Posted: 23 Sep 2006 11:56:53 pm    Post subject:

If you update your operating system to 3.10, I think implicit differentiation would become an option available under the Calc menu (listed as impDif()). However, this might apply only to TI-89 Titanium, though I'm not sure.

In any case, it wouldn't hurt to update your calculator's operating system.


Last edited by Guest on 23 Sep 2006 11:57:17 pm; edited 1 time in total
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DarkerLine
ceci n'est pas une |


Super Elite (Last Title)


Joined: 04 Nov 2003
Posts: 8328

Posted: 24 Sep 2006 10:31:20 am    Post subject:

trigkid213 wrote:
Thanks.

[EDIT]
I wrote a program to do implicit differentiation and I wanted to know if it's possible to display an answer on the home screen instead of the I/O screen (I know 84 BASIC but I'm not very familiar with 89).  Also, is it possible to graph a function like yx^2+y^2=2x without solving for y?
[post="88847"]<{POST_SNAPBACK}>[/post]
To display an answer on the home screen, make a function (you can't change a program into a function, but you can make a new function and recall a program into it). You'll have to use Local variables everywhere, but that's a good idea to do anyway. So when the function returns an answer, that answer will be displayed on the home screen.

You can't graph an implicit equation (it's not, in point of fact, a function) that easily. You can however, do the following:

Code:
y*x^2+y^2=2x->eqn
zeros(left(eqn)-right(eqn),y)->y1(x)


Last edited by Guest on 24 Sep 2006 10:31:34 am; edited 1 time in total
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