Science talk:Math Exam Resources/Courses/MATH101/April 2012/Question 1 (i)

Hi Christina, thanks for the great update. I love your version more than the previous one. I was about to change sometime but just paused to confirm.

Was it intentional to have a \pm before the omitted terms in the sine expansion?

Hi, the changes are Christina's, the \pm and \mp is from me. What's wrong with it?

I simply didn't understand it, and frankly I haven't seen people using that for omitting terms for the sine series. Perhaps Stewart wrote it that way? I haven't previewed that section yet. If you think it's right, sure just let it stay. I was thinking if it was a typo and realized it couldn't be, so there was something intentional that I could not catch.

Feel free to remove it. We should use the notation the students would be most comfortable with. It is just here to indicate the alternating signs of the following terms.

The key hint, to use McLaurin series is missing. The hint about sin(y)/y should be a second hint rather. In fact, it would be less confusing if it was y/sin(y) instead. The solution with L'Hospital does not work at all, due to the chain rule in the denominator. Hence the presented solution is not "the quickest way" but the only way to solve this.

Thanks, please feel free go ahead to make the changes you envisioned. I agree enough to let you take over. I don't have time to implement it myself now.

The L'Hospital rule does invoke chain rule and possibly "impossibly-many" complications, however, a simple call to an algebra system gives the denominator to be something like (smaller terms) + 120*x*cos(x^5). So it either requires an inhuman length of calculation or an understanding to ignore "higher order terms" which is not probably not available to most students. (The numerator is simple though, and 4 differentiations suffice to end the case).

So I agree we should simply omit it and say it's "impossible", in some sense.

Thanks, please feel free go ahead to make the changes you envisioned. I agree enough to let you take over. I don't have time to implement it myself now.

The L'Hospital rule does invoke chain rule and possibly "impossibly-many" complications, however, a simple call to an algebra system gives the denominator to be something like (smaller terms) + 120*x*cos(x^5). So it either requires an inhuman length of calculation or an understanding to ignore "higher order terms" which is not probably not available to most students. (The numerator is simple though, and 4 differentiations suffice to end the case).

So I agree we should simply omit it and say it's "impossible", in some sense.

Much better, thank you Christina.