Question

the editor of your school magazine has asked you to prepare an inspring write up on Nelson Mandela life. Write a paragraph in 100=120 words​

Answer 1

Answer:

Sometimes it is useful to compute the length of a curve in space; for example, if the curve represents the path of a moving object, the length of the curve between two points may be the distance traveled by the object between two times.

Recall that if the curve is given by the vector function r then the vector Δr=r(t+Δt)−r(t) points from one position on the curve to another, as depicted in figure 13.2.1. If the points are close together, the length of Δr is close to the length of the curve between the two points. If we add up the lengths of many such tiny vectors, placed head to tail along a segment of the curve, we get an approximation to the length of the curve over that segment. In the limit, as usual, this sum turns into an integral that computes precisely the length of the curve. First, note that

|Δr|=|Δr|ΔtΔt≈|r′(t)|Δt,

when Δt is small. Then the length of the curve between r(a) and r(b) is

Answer 2

Answer:

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Explanation:

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