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Z
zhulaojianke1-Visitor
1-Visitor
March 9, 2013
Solved

limit problem in mathcad 15

  • March 9, 2013
  • 3 replies
  • 28996 views

I use mathcad 15 M020 to quest the limitation of:

(1+2^n+3^n)^(1/n), n-->infinity

and the answer should be 3, but in mathcad it seem can not calculate it.

and I try it on the Prime M010, false too.

Why? and How should I solve this problem?

My pc system is Win7 ultimate.

Best answer by zhulaojianke

Good work Alan! You have find a really very very good solution!

limiterrorsolution.jpg

3 replies

H
HarveyHensley12-Amethyst
12-Amethyst
March 9, 2013

Works fine in MC 15 050...don't know about 010. I used the left hand limit from the toolbar, but all limit directions worked.

limit.png

W
Werner_E25-Diamond I
25-Diamond I
March 9, 2013

Harvey Hensley wrote:

Works fine in MC 15 050...don't know about 010. I used the left hand limit from the toolbar, but all limit directions worked.

Guess it is M020.

But crazy effect as I tried it myself, too (MC15 M020), but to no avail. Whats different?

limit1.png

Z
zhulaojianke1-VisitorAuthor
1-Visitor
March 10, 2013

En, my result is like Werner's.

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
March 10, 2013

朱 欣研 wrote:

I use mathcad 15 M020 to quest the limitation of:

(1+2^n+3^n)^(1/n), n-->infinity

and the answer should be 3, but in mathcad it seem can not calculate it.

My studens always check limits with plots. If it is possible!

LimPlot.png

Z
zhulaojianke1-VisitorAuthor
1-Visitor
March 10, 2013

No, I use your method to plot the f(n), the "n" can not reach 1000, and when I calculate f(1000), it return an error----Trying to caiculate the function, found a number with an order of magnitude greater than 10 ^ 307.

limiterror.jpg

Sorry, my mathCAD' error message is Chinese.

And when I calculate the lim(f(n)) n-->100000, my computer crashed.

It seemly that MC15M020's limit symbolic system isn't work on the right way.

Z
zhulaojianke1-VisitorAuthor
1-Visitor
March 10, 2013

Another interesting scene, from the plot I can assume that when f`(n)=0, the f(n) is on the limit point.

and...

limiterror2.jpg

The error message is "The variable is undefined".

and then I try to find the maximum of n:

limiterror3.jpg

It seems that the limitation symbolic calculation has used a numerical calculation method.

J
jkowalski1-Visitor
1-Visitor
March 10, 2013

I'm have Windows 7 home edtion 4GB ram ,Mathcad 15.0 (15.0.0.436 [006041742]) version and Mathcad Prime 2 F000 (2012.02.17.RC06/2.0.0.176). Work fine to me.

W
Werner_E25-Diamond I
25-Diamond I
March 10, 2013

That's a confusing phenomenom. Does it work for you with more than three summands? I think if you add more and more summands Mathcad will fail eventually. I don't think its able to simplify s(k) to k, right?

As far we have three for which it works (Harvey, Valery, Jan) and two for which it doesn't the original poster and me).

How far (speaking of k) can you go with the value of k until MC fails?

limit2.png

J
jkowalski1-Visitor
1-Visitor
March 10, 2013

result-limit.gif

For k = 100 the result is, but the larger k this requires greater computing power (large CPU time) and that's why I do not know when mathacad not calculate this.

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