Small query about L'Hopital's. (1 Viewer)

[Sy123]

Say for a question like:



It was Q1 Integation for a trial paper, I knew you just needed to do t=tan(x/2), but I decided to try and find another way:



Then you get to the point of:



Am I allowed to just say the limit evaluates to zero by L'Hopital's? I was wondering whether the stance for it would be different for a question like this where it doesnt really ask you calculate the limit.

Thanks

 

[asianese]

Well....strictly speaking the syllabus says nothing of L'Hopital's rule and it should only be used as a check method. If your teachers are mathematicians they will probably accept the answer, but since you haven't proved it, nor is it given, it is safer to guarantee that you'll gain marks by using a t-substitution.

 

[Trebla]

Usually the limits can be evaluated without L'Hopital's rule (in this case use half angles to get the result). Generally if you're using a result outside the syllabus you will need to derive it within the constraints of the syllabus.

 

[Sy123]

Well....strictly speaking the syllabus says nothing of L'Hopital's rule and it should only be used as a check method. If your teachers are mathematicians they will probably accept the answer, but since you haven't proved it, nor is it given, it is safer to guarantee that you'll gain marks by using a t-substitution.

True, my teacher doesn't have a problem with it fortunately. HSC markers on the other hand.....

Usually the limits can be evaluated without L'Hopital's rule (in this case use half angles to get the result). Generally if you're using a result outside the syllabus you will need to derive it within the constraints of the syllabus.

Good idea, thank you. I guess I was a bit too hasty with L'Hopitals, I should of probably never learnt it lol.

 

[asianese]

Truth is I haven't actually had an opportunity to evaluate a limit with L'Hopital's (as a 'sledgehammer') in any HSC before... which says something about its applicability..