Calculus

The measurements of the base and altitude of a triangle are found to be 36 and 50 centimeters, respectively. The possible error in each measurement is 0.25 centimeter. Use differentials to approximate the possible propagated error in computing the area of the triangle.

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  1. A=.5bh

    dA=.5b*dh +h*.5db

    Error = dA= .5(36)(.25)+.5(50)(.25)=10.75

    Note: with given measurements, A = .5*36*50=900

    If you are off by .25, A=.5*36.25*50.25=910.78125. Therefore you'd be off by 10.78125. Does this help to see how your estimate with differentials makes sense?

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