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IB MAI HL Calculus Topic 5.1 Differentiation (id: bd2079738)

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admin 发表于 2024-2-24 23:39:41 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Calculus Topic 5.1 Differentiation,类别为 IB数学

[填空题]
The cross-sectional view of a two-lane road tunnel system iyf 2.,d cc6qkmt(c6wf( pd95ff xe,b tm8h9sws shown on the axes below. The left and right lane tunnels are separated by a 2 metre thick concrete wall. The right-hand tunnel passes through the points A, B, C and D and its height, in metres, above the base sfb8t f9(p e9,x5hwdm of the tunnel, is modelled by
$ f(x)=-0.04 x^{3}+0.41 x^{2}, 4 \leq x \leq 10$ , relative to an origin O .

Point A has coordinates (4,4) and point $ \mathrm{D} $ has coordinates (10,1) .
1. Find the height of the right-hand tunnel when:
1. x=6 ;f(6)=  .
2. x=8 .f(8)=  .

The left-hand tunnel can be modelled by a function g(x) , found by reflecting f(x) in the line x=3 .
2. Find the equation of g(x) .
3. 1. Find $g^{\prime}(x)$ .
3.2. Hence find the maximum height of the left-hand tunnel.The maximum height of the left-hand tunnel is approximately   m.
4. 1. Write down an integral which can be used to find the cross-sectional area of the left-hand tunnel.
2. Hence find the combined cross-sectional area of both tunnels.
The combined cross-sectional area of both tunnels is approximately   m$^2$.




参考答案:
空格1: 6.12±1%空格2: 5.76!num1%空格3: 6.38±3%空格4: 61±4%


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