# d

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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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