Calculator doesn't work for this kind of equation?

[Mao]

When Solve and Int don't give you what you want, it's often because these problems cannot be solved using algebra (there are a lot of problems like this). Solve and Int both utilize an algebraic solver, which tend to not work for anything too complicated.

Numerical methods however works wonders.

nint does the same thing as int, except it's numerical (like Euler's method, a bit different but that's all under the hood, with ridiculously small stepsize and works amazingly fast).
nsolve does the same thing as solve, except it's numerical (specialist doesn't cover any root-finding algorithms, but it's pretty clever)

That problem in the first post can be solved fairly efficiently in one line with

Code: [Select]

nsolve(nint(4.9*(1-e^(-2t)),t,0,x)=1200,x)|0<x


[m@tty]

nsolve does the same thing as solve, except it's numerical (specialist doesn't cover any root-finding algorithms, but it's pretty clever)

Is it a form(or extension) of the Newton-Raphson method that is covered in MUEP?

[Mao]

nsolve does the same thing as solve, except it's numerical (specialist doesn't cover any root-finding algorithms, but it's pretty clever)

Is it a form(or extension) of the Newton-Raphson method that is covered in MUEP?

That's one of the introductory methods. Every method have its own convergence problems for some special cases. I'm not too sure what method the TI uses, it most probably will use a combination of methods, and uses some criteria to determine which method might work best at each iteration.

[m@tty]

nsolve does the same thing as solve, except it's numerical (specialist doesn't cover any root-finding algorithms, but it's pretty clever)

Is it a form(or extension) of the Newton-Raphson method that is covered in MUEP?

That's one of the introductory methods. Every method have its own convergence problems for some special cases. I'm not too sure what method the TI uses, it most probably will use a combination of methods, and uses some criteria to determine which method might work best at each iteration.

It was ingenious and elegant, except where it didn't work...

Hmm, interesting.

[Mao]

nsolve does the same thing as solve, except it's numerical (specialist doesn't cover any root-finding algorithms, but it's pretty clever)

Is it a form(or extension) of the Newton-Raphson method that is covered in MUEP?

That's one of the introductory methods. Every method have its own convergence problems for some special cases. I'm not too sure what method the TI uses, it most probably will use a combination of methods, and uses some criteria to determine which method might work best at each iteration.

It was ingenious and elegant, except where it didn't work...

Hmm, interesting.

NR is annoying in the sense that you have to know the derivative to find the root. There are several other methods with similar computational complexity (i.e. number of operations or time required) that doesn't require much. Have a look at the wiki page if you are interested.

[m@tty]

I was talking about the whole concept of following tangents to narrow down the root.

Maybe I will have a look at the wiki page . . .

[3Xamz]

The question is worth three marks, so it's not expected for the calculator to just spit out the answer.
Even if it did and you wrote it down, you'd only get 1/3 marks

The whole point of it being a 3 point question, is that the student must manually anti derive it, and simplify it before entering the straightforward (but complicated due to the nature of the numbers) of an equation into the calc to get the answer.

This gives you the time value, then just draw up a triangle to get the distance components and voila!

[jto1292]

The question is worth three marks, so it's not expected for the calculator to just spit out the answer.
Even if it did and you wrote it down, you'd only get 1/3 marks

The whole point of it being a 3 point question, is that the student must manually anti derive it, and simplify it before entering the straightforward (but complicated due to the nature of the numbers) of an equation into the calc to get the answer.

This gives you the time value, then just draw up a triangle to get the distance components and voila!

Ermm, actually, I believe finding the time alone was 1 mark's worth. That by far took the longest. The second mark would've probably been awarded once a right angle triangle was drawn and the distance of the boat from O was found. Finally the third mark would've been at pythagoras' theorem for the correct answer. The time that was needed to subsequently gain all three marks was an issue to find using CAS. All I'm saying is it shouldn't have been such a time-consumer. Exam 2s are already packed as it is. We don't have time to waste manually subbing in possible values for t until we get the desired answer of 1200. ALTHOUGH apparently, problem solved by putting a domain for t at 200 - 300.

[Mao]

The whole point of it being a 3 point question, is that the student must manually anti derive it, and simplify it before entering the straightforward (but complicated due to the nature of the numbers) of an equation into the calc to get the answer.

I'm not sure I agree with that. I'm not an examiner, but when I did spec I never wrote down 'intermediate' answers. I outlined my method (explain what the integral describes, define variables, which equations to solve), did not do much by hand (at all), and gave the calc input and wrote down the final answer.

I believe the marks are in the method, not manual operations. If you can present the correct method and relied on the calculator to evaluate things, I don't think there should a problem with it at all.

[kyzoo]

...Siff 2009 is an easy exam =.=

[chansthename]

Is it a form(or extension) of the Newton-Raphson method that is covered in MUEP?

I remember that, I liked how it got double the decimal places (approximately) every step, totally forgotten it now but It was cool at the time.