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Newton's theory of gravitation states that the weight of a person at elevation x feet above sea level is W(x) = PR2/(R+x)². where P is the person's weight at sea level and R is the radius of the earth (approximately 20,900,000 feet). Find the linear approximation of W(x) at x = 0. Use the linear approxima- tion to estimate the elevation required to reduce the weight of a 120-pound person by 1%.
โจทย์ Newton Method
Newton's theory of gravitation states that the weight of a person at elevation x feet above sea level is W(x) = PR2/(R+x)². where P is the person's weight at sea level and R is the radius of the earth (approximately 20,900,000 feet). Find the linear approximation of W(x) at x = 0. Use the linear approxima- tion to estimate the elevation required to reduce the weight of a 120-pound person by 1%.