Going back to integrating squareroot(tangent(x)), obviously the first step should be a substition like z = tangent (x). That would lead to squareroot(z)/(1+z^2). Strangely, if you give the TI89 that to integrate, it'll do it in a couple of seconds. So why does it take 20 minutes before hand?
The Classpad still can't do that integral. If you go one more step, to y^2 = z, you'll get 2*y^2/(1+y^4), and it can finally do that one.
In my experience even with Maple, though, I've found that you often need to give "nudges" to these Computer Algebra Systems to get them to work or do what you want them to do.
As for Taylor Series on the 49G+, this is a straightforward program to do it:
%%HP: T(3)A(R)F(.);
RPL>
\<< \-> F X O P
\<< F 0 O
FOR I DUP X P = EVAL SUBST EVAL I ! / X P - I ^ * SWAP X \.d
NEXT DROP 0 'O-1' EVAL
FOR I +
NEXT
\>>
\>>
It probably will only work in RPN mode. First enter the function you want to expand, then the variable it should be expanded in, then the number of terms, and finally the point it's expanded about.
As I said, it's very straightforward (I suspect that the 49G+'s built in taylor function uses pattern recognition to speed it up), and hence somewhat slow, but it works.
"Perhaps one did not want to be loved so much as to be understood."
-Orwell
The Classpad still can't do that integral. If you go one more step, to y^2 = z, you'll get 2*y^2/(1+y^4), and it can finally do that one.
In my experience even with Maple, though, I've found that you often need to give "nudges" to these Computer Algebra Systems to get them to work or do what you want them to do.
As for Taylor Series on the 49G+, this is a straightforward program to do it:
%%HP: T(3)A(R)F(.);
RPL>
\<< \-> F X O P
\<< F 0 O
FOR I DUP X P = EVAL SUBST EVAL I ! / X P - I ^ * SWAP X \.d
NEXT DROP 0 'O-1' EVAL
FOR I +
NEXT
\>>
\>>
It probably will only work in RPN mode. First enter the function you want to expand, then the variable it should be expanded in, then the number of terms, and finally the point it's expanded about.
As I said, it's very straightforward (I suspect that the 49G+'s built in taylor function uses pattern recognition to speed it up), and hence somewhat slow, but it works.
"Perhaps one did not want to be loved so much as to be understood."
-Orwell
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