Show that the average value of sin^2t over [0,2pi] is equal to 1/2. Without further calculation determine whether the average value of sin^2t over [0,pi] is equal to 1/2.
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Show that the average value of sin^2t over [0,2pi] is equal to 1/2. Without further calculation determine whether the average value of sin^2t over [0,pi] is equal to 1/2.
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- Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?What is the average value of the function (arctan x)^2/1+x^2 over [1,square root 3]?The measurment of the radius of the end of a log is found to be 28 inches, with a possible error of 1/4 inch. Use differentials to approximate the possible propagated error in the computing the area of teh end of the log. Then determine the relative error (as a %). Round to 2 decimal places.
- the measurement of the radius of the end of a log is found to be 20 inches, with a possible error of1/8 inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.The length and width of a rectangle are measured with errors of at most 3% and 5%, respectively. Use differentials to approximate the maximum percentage error in the calculated area.The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch. Use differentials to approximate the possible propagated error and percent error in computing the volume of the cube. Show all work
- 5) The length of the side of a square floor tile is 15 cm, with a possible error of 0.05 cm. Using differentials, estimate the possible propagated error in the computed area of the tile.Suppose the measurement of the side of a square is to be 30 cm with an error of 0.03 cm. Use differentials to estimate the propagated error in computing the area of the square.3) Use differentials to estimate the relative error in the lateral surface area of a right circular cylinder if the diameter is measured to be 10 in. with a possible error of 0.01 in. and the height is equal to its diameter.
- For a given triangle, side y is measured as 10 cm, the horizontal side x as 20 cm and the included angle as 30o. There is an error of as much as 0.2 cm on each of the sides and 1o in the included angle. Use total differentials to estimate the error in the computed area of the triangle.The radius of a sphere is measured as 9 centimeters, with a possible error of 0.025 centimeter. (a) Use differentials to approximate the possible propagated error in computing the volume of the sphere. (b) Use differentials to approximate the possible propagated error in computing the surface area of the sphere. (c) Approximate the percent errors in parts (a) and (b)The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch. (a) Use differentials to approximate the possible propagated error in computing the volume of the cube. (b) Use differentials to approximate the possible propagated error in computing the surface area of the cube. (c) Approximate the percent errors in parts (a) and (b)