HP 50g Limit Help

[Carsen]

Greetings everyone!

I cannot get my HP 50g to find the limit as X approaches 0 when...

f(x)=(cos(x)-1+(1/2)*x^2)/x^4.

When I try to solve it on the calculator, regardless if in AOS or RPN, I always get the response "Insufficient order" from the calculator and puts a "?" as my answer. I know the problem has an answer because I solved it by hand. The answer is 1/24.

I have been able to find every limit I have encountered with my HP 50g until now so this is a very unexpected problem that surfaced. I have spent about 30 minutes trying to figure it out but came out with nothing. Therefore, I am hoping I can count on everyone's help here at the Museum, especially since I don't have anymore time to spend on this issue. (College. Need I say more?). Plus, it's getting rather frustrating but I just got to keep remembering that it's problems like these that makes me learn more about my HP 50g.

Thank you all so much in advance!

[Pascal]

Hi!

The default order used by lim is less than 4, so it is too low for your example.
Put your function on stack level 3, 'X=0' on level 2, and the required order (4 at least) on level 1, then execute SERIES, instead of lim.

Best regards.

[Simone Cerica]

as suggested by Pascal:

'(COS(X)-1+X^2/2)/X^4' 'X=0' 4 SERIES --> { :Limit: '1/24' :Equiv: '1/24' :Expans: '1/24' :Remain: h } 'h=X'

so '1/24' is the answer

[jebem]

(02-23-2017 05:59 AM)Carsen Wrote:  I cannot get my HP 50g to find the limit as X approaches 0 when...

f(x)=(cos(x)-1+(1/2)*x^2)/x^4.

When I try to solve it on the calculator, regardless if in AOS or RPN, I always get the response "Insufficient order" from the calculator and puts a "?" as my answer. I know the problem has an answer because I solved it by hand. The answer is 1/24.

A little off topic, but my HP Prime came out with the correct answer on both environments (Home and CAS), by just typing your function.
I know it's not a RPL machine and it doesn't have the 50G heritage, but it's a HP as well and highly oriented to the education market.

[Carsen]

Pascal and Simone! Thanks so much! It worked perfectly the first time I tried it out. But now I have one more question in the functionality of the SERIES function. I do not understand the concept of the "order" that you put on level 1 of the stack before executing the function SERIES. How do I know what number of order to use? Keep in mind that I have not learned anything about Taylor Polynomials and I don't know too much about limits yet. I am only in Calculus 2.

Jebem. Yeah, I would LOVE to get a Prime mainly for it's touchscreen because it is so useful when graphing. But I am thinking of getting a HP 48gx first while I can because there are only so many of them left out there. Plus, I don't have too much of a budget for buying calculators...yet

Again, Thank you all for helping me out!