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Calculus help!!Suppose an earthquake is measured with a magnitude of 6 on the Richter scale with an error of at most 2%. Use differentials to find the error in the intensity of the earthquake

  • d -

    change logs to numbers.
    1E6(1+-.02)
    now, go to logs.
    remember that log(ab)=log a+logb
    Intensity=6 +log.98 to 6 +log(1.02)

    The error is the difference, so
    error=log1.02-log.98= .009+.009=.018

    You can work it more accurately. Now differentials:
    Error=highentensity-lowintensity
    dError=dHigh-dlow=log1.02-log.98

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