# calculus

posted by jin

The circumference of a sphere was measured to be 78.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.

Estimate the relative error in the calculated surface area.

1. drwls

The relative error in area is, to first approximation, twice the relative error in a linear dimension.

That is because
(delta A)/A = (1 + epsilon)^2 - 1
= 1 + 2 epsilon + epsilon^2 - 1
= 2 epsilon
when epsilon << 1

2*0.5/78 = 1/78 = 1.3%

## Similar Questions

1. ### Calculus

The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area?
2. ### Calculus

The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area?
3. ### CAL

THe circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use the linear appoximation to estimate the maximum error in the calculated surface area. and estimate the relative error in the calculated …
4. ### Calculus

The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area
5. ### math

The circumference of a sphere was measured to be 82.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface …
6. ### CALCULUS

The circumference of a sphere was measured to be 83000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. ________________ Estimate the relative error in the …
7. ### Math

The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface …
8. ### Math

The circumference of a sphere was measured to be 89.000 cm with a possible error of 0.50000 cm. A. Use linear approximation to estimate the maximum error in the calculated surface area. B. Estimate the relative error in the calculated …
9. ### Math

The circumference of a sphere was measured to be 89.000 cm with a possible error of 0.50000 cm. A. Use linear approximation to estimate the maximum error in the calculated surface area. B. Estimate the relative error in the calculated …
10. ### Calculus

The circumference of a sphere was measured to be 76.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.Estimate the relative error in the calculated surface …

More Similar Questions