UNSW 1st year finals Q (1 Viewer)

[anomalousdecay]

are you sure the first question is really like that? I guess you missed a y on RHS? like

the second question can be solved, other than L'Hospital rule, using equivalent substitution like

No the first question is correct straight from my paper. I did solve it above (just had a little error though). It asks for the first two non-zero terms of the Maclaurin series for y.

Also for your second part, is that even a proper substitution? You could use it for one of the cases for using Pinching Theorem, but to me that substitution just looks a bit dodgy....

 

[FrankXie]

No the first question is correct straight from my paper. I did solve it above (just had a little error though). It asks for the first two non-zero terms of the Maclaurin series for y.

Also for your second part, is that even a proper substitution? You could use it for one of the cases for using Pinching Theorem, but to me that substitution just looks a bit dodgy....

for question 1: so it was not "find y", it was the approximation solution by series. that's totally different. if the equation was correct, no way to find the analytic solution!
for question 2: yes my substitution works and is correct. as a matter of fact, only when it is a factor, i can do equivalent substitution; and for many questions substitution can make solution a lot easier. other substitutions are

 

[D94]

No the first question is correct straight from my paper. I did solve it above (just had a little error though). It asks for the first two non-zero terms of the Maclaurin series for y.

Also for your second part, is that even a proper substitution? You could use it for one of the cases for using Pinching Theorem, but to me that substitution just looks a bit dodgy....

Well, that should have been mentioned by the OP, because you haven't 'solved' it, but rather found an approximation. Two completely different things.

 

[anomalousdecay]

for question 1: so it was not "find y", it was the approximation solution by series. that's totally different. if the equation was correct, no way to find the analytic solution!
for question 2: yes my substitution works and is correct. as a matter of fact, only when it is a factor, i can do equivalent substitution; and for many questions substitution can make solution a lot easier. other substitutions are

Sorry about that lol.

Yeah I'm not too familiar with the substitution method you showed :/
Probably is fine because it worked, but haven't actually substituted like that before with limits.

Well, that should have been mentioned by the OP, because you haven't 'solved' it, but rather found an approximation. Two completely different things.

Yeah true. That's why Maple and MATLAB didn't give anything out.

Paper actually says "find the first two non-zero terms" not solve. My bad lol.

 

[D94]

Yeah true. That's why Maple and MATLAB didn't give anything out.

Paper actually says "find the first two non-zero terms" not solve. My bad lol.

Yeah I was trying to use the ODE methods taught in first year to solve that but nothing was working. I have long since forgotten the Maclaurin series but I know it's closely related to the Taylor series.

 

[anomalousdecay]

Yeah I was trying to use the ODE methods taught in first year to solve that but nothing was working. I have long since forgotten the Maclaurin series but I know it's closely related to the Taylor series.

Its Taylor series about x = 0. So just do it normally, except you substitute in f (0), f '(0), etc.

And instead of (x-a)^n its (x-0)^n = x^n.

Have a go at it. Its a decent question which caught me off guard in the exam (but I got most of it out, despite the silly errors). A lot of other people I know didn't attempt it.

 

[seanieg89]

Yeah I'm not too familiar with the substitution method you showed :/
Probably is fine because it worked, but haven't actually substituted like that before with limits.

They are just leading order Taylor approximations.

 

[FrankXie]

These explainations make the question make more sense. lol

I was trying to say the question might be

solve or find the ananytic solution of

 

[anomalousdecay]

They are just leading order Taylor approximations.

Yeah no clue we could do that (have never been taught to take the first approximation as a substitution for a limit).

These explainations make the question make more sense. lol

I was trying to say the question might be

solve or find the ananytic solution of

Hmm well there is a marathon thread in here, maybe I'll quote this and have a go at it later.