When you are at a height x above the surface of the earth, your weight can be found by the following formula: W(x) = mg (1 + x/R) −2 , where m is the mass of your body, g is the acceleration due to gravity, and R is the radius of the earth. For example, W(0) is your weight when you are on the surface of the earth and W(R) is your weight when you are at the height R above the surface of the earth (yes, you are far away from the earth’s atmosphere). In this question, we will approximate W(0) and W(R). (a) Find L0(x), the linear approximation of W(x) at x = 0. (b) Use L0(x) to approximate W(0) and W(R). Which approximation is more accurate? Why? (c) Find LR(x), the linear approximation of W(x) at x = R. (d) Use LR(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
When you are at a height x above the surface of the earth, your weight can be found by the following formula:
W(x) = mg (1 + x/R) −2 ,
where m is the mass of your body, g is the acceleration due to gravity, and R is the radius of the earth.
For example, W(0) is your weight when you are on the surface of the earth and W(R) is your weight when you are at the height R above the surface of the earth (yes, you are far away from the earth’s atmosphere).
In this question, we will approximate W(0) and W(R).
(a) Find L0(x), the linear approximation of W(x) at x = 0.
(b) Use L0(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
(c) Find LR(x), the linear approximation of W(x) at x = R.
(d) Use LR(x) to approximate W(0) and W(R). Which approximation is more accurate? Why?
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