Solution: We have . We have measurements and .

Our best guess for , which we denote by , is given by:

.

We approximate the error in this calculation, due to the error in the measurements of and using differentials:

.

We therefore need to differentiate partially with respect to and . The quickest way is to rewrite:

. Thus we get:

and

.

Alternatively, using the Quotient Rule on :

, and

.

Therefore

.

Evaluating the derivatives at the measurements:

The absolute value of is , so

.

It is good practise to round this to one significant figure because it is a rough approximation (not applicable here) and also, with the calculation, , to match the precision: in this case two decimal places: everything beyond the second decimal place is within the margin of error.

Answer therefore,

.

This question is missing context that would tell us the units. If there are units they must be included.

Regards,

J.P.

I’m one of your maths student and was wondering if you could help with the question we were doing for tutorial. It’s question 5 of the last Test 2 paper you sent us. I’ve attempted it and just wanted to see if I was right and if not if you could show or tell me where I went wrong please.

]]>If you divide above and below you by you get:

.

Regarding Q. 2, area doesn’t come into it at all.

Regarding Q. 3, you have the slope correct but note the question doesn’t ask for anything more.

Regarding Q. 4 you need to know that:

increases with .

decreases with .

For Q. 5, you lose one mark for not including the unit. After that, please round the error to one significant figure (because using the differential is a rough approximation):

and match the precision (because beyond this is within margin of error: no decimal places in this case) with the calculated value:

,

so your answer reads

.

Regards,

J.P.

Could you correct these for me please and tell me how to do Q4 aswell.

Thanks a lot.

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