1. Use linear approximation to approximate 9. Make sure to indicate what function and initial value...

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1. Use linear approximation to approximate 9. Make sure to indicate what function and initial value you chose for the linear approximation. 2. The Great Pyramid of Giza was originally 280 cubits tall with a square base that was 440 cubits by 440 cubits. Suppose the height of the pyramid is shrinking by approximately 0.7 cubits per century and the base side length remains proportional to the height. How fast is the volume decreasing when the height is 266 cubits? Use the fact that the volume of a square pyramid is V = sh, where s is the base side length and h is the height. 3. Galileo estimated the radius of the earth to be 3,500 miles. If the largest possible error in his measurement is 500 miles, use differentials to estimate the maximum possible error in the calculated volume of the earth. 3 Use the formula V = for the volume of the earth. 4. Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the function (x) = x4 - 8x +5 on the interval [0,2]. 5. A tank with rectangular base and rectangular sides is open at the top. The tank must be 1 meter wide and have a volume of exactly 3 cubic meters. Material for the sides of the tank costs $2 per square meter and material for the bottom costs $3 per square meter. What are the dimensions for the least expensive tank? 1. Use linear approximation to approximate 9. Make sure to indicate what function and initial value you chose for the linear approximation. 2. The Great Pyramid of Giza was originally 280 cubits tall with a square base that was 440 cubits by 440 cubits. Suppose the height of the pyramid is shrinking by approximately 0.7 cubits per century and the base side length remains proportional to the height. How fast is the volume decreasing when the height is 266 cubits? Use the fact that the volume of a square pyramid is V = sh, where s is the base side length and h is the height. 3. Galileo estimated the radius of the earth to be 3,500 miles. If the largest possible error in his measurement is 500 miles, use differentials to estimate the maximum possible error in the calculated volume of the earth. 3 Use the formula V = for the volume of the earth. 4. Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the function (x) = x4 - 8x +5 on the interval [0,2]. 5. A tank with rectangular base and rectangular sides is open at the top. The tank must be 1 meter wide and have a volume of exactly 3 cubic meters. Material for the sides of the tank costs $2 per square meter and material for the bottom costs $3 per square meter. What are the dimensions for the least expensive tank?