Numerical Methods Help Please

Hi everyone,

I am attempting past paper questions for MEI NM and I need help answering this question:

More specifically, I need help with the last part. I can do everything but give the answer to a justifiable number of decimal places. What d.p. do I give my answer to?

Reply 1

joostan

Original post by Malabarista

Hi everyone,

I am attempting past paper questions for MEI NM and I need help answering this question:

More specifically, I need help with the last part. I can do everything but give the answer to a justifiable number of decimal places. What d.p. do I give my answer to?

How many d.ps was the data you were given to?
The final answer should be quoted to the same no. of d.ps

(edited 11 years ago)

Reply 2

Malabarista

Original post by joostan

How many d.ps was the data you were given to?
The final answer should be quoted to the same no. of d.ps

It says in the question that the points were given to 4 d.p. The answer however, cannot be given to 4 d.p. The markscheme gives the answer to 2 d.p. although, I've done the 'long way' and worked out the interval estimates at each stage and really it can only be given correct to 1 d.p. which the markscheme also accepts.

Reply 3

Malabarista

Here's the markscheme by the way...

Reply 4

joostan

Original post by Malabarista

Ohh, you've used the data given to then calculate the gradient: - In which case the manner in which the number of sfs, should be reduced. Tbh I'd have quoted to 3s.f.s and had done with it, but since the question asks you to explain yourself I'd have done what you did.

Reply 5

Malabarista

Original post by joostan

To get 2.8, 1 d.p., I had to spend a fair amount of time working out interval estimates back from when I calculated the gradients every time I did a subtraction on the approximations. However, I also took a similar approach and worked out the interval estimates assuming that the gradient estimates were also correct to 4 d.p. (which in reality they're not) and got to an interval estimate from which I could say that the answer was 2.77, 2 d.p.

So the second way I tried it seems to work but seeing as there's no substantial explanation in the back it's hard to know if that's the correct approach or not.

Reply 6

joostan

Original post by Malabarista

Well tbh the whole thing is an exercise in futility - if they gave you the function, you could just differentiate it, or work out a suitable equation then differentiate that.
Its just about jumping through hoops. If the shorter method is acceptable, then I'd use that.
The longer way may be closer to the truth, but that's not really what they're looking for :tongue:

Reply 7

Malabarista

Original post by joostan

Indeed, the steps in x in the data are even so for absolute overkill we could have used the Newton interpolating polynomial on it and differentiated that. I'm more concerned with knowing if the shorter method is correct in every case, though it could just be that it lead me to the correct answer by coincidence. I can't see any other way of doing it though, so if it comes up in the exam I'll just roll with that.