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    • Thread Starter

    Hey guys,

    I am stuck and would appreciate some help!

    1) f(x)= sin1/2x + cos1/3x

    write down another value of X (not 0) for which f(x)=f(0) and f'(x)=f'(0)

    So I got sin1/2x + cos1/3x =1
    then I have no idea what to do LOL!

    I also got 1/2cos1/2x- 1/3sin1/3x =1/2

    Again I have no idea how to simplifiy or anything...

    Help would be appreciated and plus rep given.

    Consider sin1/2x + cos1/3x =1.

    If x=even multiple of pi, then the sine term vanishes.
    So which values of x=2pi, 4pi, 6pi,...etc give cos(x/3)=1 ?
    Clearly x=6pi, 12pi, 18pi,...etc will work.

    Similarly for 1/2cos1/2x- 1/3sin1/3x =1/2, the sine term vanishes for x=multiples of 3pi = 3pi, 6pi, 9pi, 12pi,...etc
    So which of these values give cos(x/2)=1 ?

    Which solution is common to both equations?
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