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Solve the given problems by finding the appropriate differential.Show that an error of $2 \%$ in the measurement of the radius of a ball bearing results in an error of approximately $6 \%$ in the calculation of the volume.

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 8

Differentials and Linear Approximations

Derivatives

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Lectures

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In mathematics, precalculu…

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01:20

Use the differential formu…

09:07

Volume and Surface Area Th…

02:05

02:04

For the following exercise…

00:21

Describe and correct the e…

10:50

The circumference of a sph…

04:38

06:20

(a) Use differentials to f…

01:24

00:42

So for this problem over given b side length of the cube as well as the error in that side length. Ah, and we want to know what the error in our volume would be. I'm so we know that the formula for our error is that our error, which is D Y, is going to be equal to f Prime of x d x. I mean so since we know that we are finding the volume here, that means that our function of V of X is there volume as a function of our side. Lee is equal to X Cube. But that's just because of the fact that we know we have a cube here. Um And so if we find the derivative here, TV with respect to D. X is going to be equal to three x squared. Um And so when we change it into this formula right here, we get Devi is equal to three x squared DX um and then from our formula, we know that X is going to correspond to whatever our initial measurement is. That's going to be six and D. X is our error in that initial measurements, which is going to be 0.2 So when we plug this in, we find that our air error is equal to three sometimes X, where, which is six word times. DX, which is plus or minus 0.2 inches. And when we saw if we find that our error is equal to inner, volume is equal to plus or minus 2.16 inches.

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