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calculus

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Need help asap! what is the limit as x approaches 0 of -x/tan(3x) ?

  • calculus -

    You should have either proved or collected several basic trig limits
    e.g.
    limit sinx/x as x---> 0 = 1
    also
    lim tanØ/Ø as Ø ---> 0 = 1 which implies lim Ø/tanØ as Ø ---> 0 = 1

    so let's make your question look like that

    lim -x/tan(3x)
    = lim -3x/(3tan(3x))
    = lim (-1/3) [(3x)/tan(3x)] , (where 3x = Ø)
    = lim (-1/3) [Ø/tanØ]
    = (-1/3)(1)
    = -1/3

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