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calculus

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Lim sin2h sin3h / h^2
h-->0

how would you do this ?? i got 6 as the answer, just want to make sure it's right.

and i couldn't get this one (use theorem 2)
lim tanx/x
x-->0



and also this one (use squeeze theorem to evaluate the limit)

lim (x-1)sin Pi/x-1
x-->1

  • calculus -

    the first one is correct.
    Here is a simple way to check your limit answers if you have a calculator

    pick a value very "close" to your approach value, in this case I would pick x = .001
    evaluate using that value, (you are not yet dividing by zero, but close)
    I got a value of 5.999985 which I would say is close to 6

    for lim tanx / x as x -->0
    = lim (sinx/cosx)/x
    = lim (sinx/x)*lim 1/cosx as x ----> 0
    = 1*1 = 1

    If you meant lim (x-1)sinπ/(x-1)
    wouldn't the last one simply be sinπ or 0 ?

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