Question

这道英文微积分数学题如何做？

An airplane is located at position (4,3,8)(4,3,8) at noon and traveling with velocity 300i+350j−k kilometers per hour.The pilot spots an airport at position (34,38,0)(34,38,0).
一架飞机在中午位于（4,3,8），行驶速度为300i + 350j-k公里每小时。飞行员位于机场（34,38,0）点

(a) How many minutes needs the plane to pass directly over the airport?
飞机需要多少分钟才能直接通过机场？
(b) How high above the airport will the plane be when it passes?
机场经过机场后有多高？

Answer 1

F(n)=∫₀ⁿ⌊t⌋dt
=∫₀¹0dt+∫₁²1dt+∫₂³2dt+⋯+∫⌊ⁿ⌋⌊n⌋₋₁(⌊n⌋-1)dt
=0+1+2+⋯+(⌊n⌋-1)
=(⌊n⌋-1)⌊n⌋/2

F(x)=∫₀x⌊t⌋dt
=∫₀⌊x⌋ ⌊t⌋dt+ ∫(⌊x⌋,x) ⌊t⌋dt
=(⌊x⌋-1)⌊x⌋/2 +∫(⌊x⌋,x) ⌊x⌋dt
=(⌊x⌋-1)⌊x⌋/2 +(⌊x⌋-x)⌊x⌋
=(3⌊x⌋-2x-1)⌊x⌋/2