Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Approximation

1. The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5 inches. What is the maximum possible error in the volume of the cube if we use this value of the length of the side to compute the volume? 2. The altitude of a right circular cone is equal to the radius of the base and is measured as 5 in with a possible error of 0.02 in. Find the greatest possible error in the computed value of the volume and the % error. 3. The intensity of the illumination, I, on an object at distance x from a light source is k I = where k is a constant. If an object is 200 ft from a light source, how much x². 2 should the distance be change to increase the illumination by 1%? 4. The diameter and height of a right circular cylinder are measured to be 5 in and 8 in, respectively. If each of these dimensions maybe in error by ±0.10 in. Fin d the greatest possible %error in the volume of the cylinder. 5. The diameter of a circle is to be measured and its area computed. If the diameter can be measured with a maximum error of 0.001 in and the area must be accurate to within 0.1 in³. Find the largest diameter for which the process can be used.
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Transcribed Image Text:1. The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5 inches. What is the maximum possible error in the volume of the cube if we use this value of the length of the side to compute the volume? 2. The altitude of a right circular cone is equal to the radius of the base and is measured as 5 in with a possible error of 0.02 in. Find the greatest possible error in the computed value of the volume and the % error. 3. The intensity of the illumination, I, on an object at distance x from a light source is k I = where k is a constant. If an object is 200 ft from a light source, how much x². 2 should the distance be change to increase the illumination by 1%? 4. The diameter and height of a right circular cylinder are measured to be 5 in and 8 in, respectively. If each of these dimensions maybe in error by ±0.10 in. Fin d the greatest possible %error in the volume of the cylinder. 5. The diameter of a circle is to be measured and its area computed. If the diameter can be measured with a maximum error of 0.001 in and the area must be accurate to within 0.1 in³. Find the largest diameter for which the process can be used.
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