http://www.forrestrace.com/square-tile-4/
the measurement of the edge of a piece of square floor tile is found to be 12 inches with a possible error of.?
0.02 inches.
a. use differentials to approximate the maxumum possible error in the area of the tile
b. use the answer from part a to estimate the relative error
c. use the answer from part b to estimate the percentage error.
Let the side of the square be x and let the error be δx.
Then the side length will be (x + δx)
So the area will be (x + δx)² = x² + 2x.δx + (δx)²
If δx = 0, the area = x².
So the maximum size the floor tile can be is x² + 2x.δx + (δx)²
Now insert the numbers: 144 + 24 X 0.02 + 0.0004 = 144.480 sq. in.
So the relative error, R.E. = {[x² + 2x.δx + (δx)²} -[x²]} / x²
which is: [2x.δx + (δx)²] / x².
Now insert the numbers:
R.E. = [24 X 0.02 + (0.02)²] / 144 = [0.48 + 0.0004] / 144 = 0.0034
And the %-age error will be: (0.0034 / 144) X 100 = 0.00236 %
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