高数题 微分 第12题
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高数题 微分 第12题
![](http://img.wesiedu.com/upload/5/09/5094c2fc2a3f642f2fabcd01d7118e55.jpg)
![](http://img.wesiedu.com/upload/5/09/5094c2fc2a3f642f2fabcd01d7118e55.jpg)
![高数题 微分 第12题](/uploads/image/z/4123950-6-0.jpg?t=%E9%AB%98%E6%95%B0%E9%A2%98+%E5%BE%AE%E5%88%86+%E7%AC%AC12%E9%A2%98)
h = 24
影子长l,tanθ = h/l,l = h/tanθ = hcosθ/sinθ,θ为t的函数
dl/dt = (dl/dθ)(dθ/dt) = [(-hsinθ)θ'(sinθ) - hcosθ(cosθ)θ']/sin²θ = -h(sin²θ + cos²θ)θ'/sin²θ
= -hθ'/sin²θ
l = 18,斜边L = 30 m,sinθ = 4/5,sin²θ = 16/25
θ = 60⁰,sin²θ = 3/4,θ' = 0.27⁰/min = 0.0047弧度/min
dl/dt = -24*0.0047/(16/25) = -0.18 m/min
即以0.18m/min的速度缩短
影子长l,tanθ = h/l,l = h/tanθ = hcosθ/sinθ,θ为t的函数
dl/dt = (dl/dθ)(dθ/dt) = [(-hsinθ)θ'(sinθ) - hcosθ(cosθ)θ']/sin²θ = -h(sin²θ + cos²θ)θ'/sin²θ
= -hθ'/sin²θ
l = 18,斜边L = 30 m,sinθ = 4/5,sin²θ = 16/25
θ = 60⁰,sin²θ = 3/4,θ' = 0.27⁰/min = 0.0047弧度/min
dl/dt = -24*0.0047/(16/25) = -0.18 m/min
即以0.18m/min的速度缩短