Hey there! Sign in to join this conversationNew here? Join for free
    Offline

    2
    ReputationRep:
    Err, have you guys don L^Hopitals yet? If you plug in x = 0 you get an indeterminate form, so differentiate and then you'll get lim x -> 0 sin(x) = 0. Hence lim x-> 0 of 1-cos(x)/x = 0
    Offline

    2
    ReputationRep:
    (Original post by barnisaurusrex)
    Err, have you guys don L^Hopitals yet? If you plug in x = 0 you get an indeterminate form, so differentiate and then you'll get lim x -> 0 sin(x) = 0. Hence lim x-> 0 of 1-cos(x)/x = 0
    I would strongly advise not using L'Hopital's rule for this question. This is because the question is essentially asking you to calculate a derivative. The question could reasonably then state 'Hence show that the cosine function is differentiable at 0 with derivative 0.' Using L'Hopital's rule would then be circular reasoning. In addition, it doesn't follow the hint given at all and is far too strong for this kind of question. I think that the question was designed to help practice limits, rather than to pull out big machinery.
    Offline

    2
    ReputationRep:
    (Original post by IrrationalNumber)
    I would strongly advise not using L'Hopital's rule for this question. This is because the question is essentially asking you to calculate a derivative. The question could reasonably then state 'Hence show that the cosine function is differentiable at 0 with derivative 0.' Using L'Hopital's rule would then be circular reasoning. In addition, it doesn't follow the hint given at all and is far too strong for this kind of question. I think that the question was designed to help practice limits, rather than to pull out big machinery.
    Well I guess that's physicists mentality vs. mathematicians. L^Hopitals gets you there perfectly fine and everything you've suggested seems overly technical and flippant. Personally I'm in favour of getting to the answer the easiest possible way, but hey, I can see if it's an analysis module then the most abstract, least intuitive way is definitely the best way
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.