1. (a) A right circular cylinder of volume V has height h and base radius r. Find the rate of change of V with respect to
(1) h, if r is kept constant.
(2) r, if h is kept constant.
(b) The base radius of a cylindrical candle is 2 cm. It is burning so that its height is diminishing at a rate of 0.5 cm / min. What is the rate of change of its volume?
2. John observes a helicopter is 260 m from him. The helicopter is flying horizontally towards him at a rate 30 m / s at an altitude of 100 m. How fast is the helicopter approaching him?
Differentiation-rate of change
2009-01-05 8:33 am
回答 (2)
2009-01-05 9:45 am
✔ 最佳答案
1. (a)V= πr^2 h (π is pi)
(1) dV/dh= πr^2 (2)dV/dr= 2πrh
(b) r = 2 cm , dh/dt= - 0.5 cm/min
=> dV/dt= πr^2 dh/dt= - 2π cm/min
2. 設helicopter與John之水平距離= x m, 直線距離L
=> L^2=100^2+x^2 ----(A)
已知 dx/dt= - 30 m/s
(A)式兩邊同對時間 t求導函數, 得
2L dL/dt= 2x dx/dt => L dL/dt= x dx/dt ---(B)
When L=260時, x^2=260^2-100^2= 240^2 => x= 240
故(B)式: 260 dL/dt= 240*(-30) =>dL/dt= - 360/13
即helicopter以每sec 360/13的速率接近John.
參考: me
2009-01-05 9:08 am
do you have numerical answer?
收錄日期: 2021-04-11 16:58:21
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