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posted by Anonymous on .
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

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=log1.02log.98= .009+.009=.018
You can work it more accurately. Now differentials:
Error=highentensitylowintensity
dError=dHighdlow=log1.02log.98