00:01
The side s of a square carpet is measured at 6 meters.
00:04
Estimate the maximum error in the area a of the carpet.
00:08
If s is accurate to within 2 centimeters.
00:11
So what this question is asking is if the measurement of side s were off by at most 2 centimeters, what would be the difference in the area from the actual value? so in order to find this error, we can use this equation from the type of, where we have f of a plus a certain delta x, which would be our error of two centimeters, minus f of a, which would be the actual value.
00:45
And that gives us delta f, and delta f signifies the error in the area value.
00:54
So in order to find delta f, we can use the linear approximation, which is shown here, it says that delta f is approximately equal to f prime at point a multiplied by delta x.
01:10
So looking back at our problem, we can define our variables where a is equal to 6 because that is the measured length of the side.
01:25
And then delta x equals 2 centimeters.
01:34
So if we convert that into meters so that the units are constant, that's 0 .02.
01:42
And now we need to define our function.
01:46
So since we're given our side length and we want to find our area length, we can use the expression fx equals x squared because of the area formula where a equals s squared...