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Differential Calculus (id: 59225a6d5)

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admin 发表于 2024-7-30 23:15:50 | 显示全部楼层 |阅读模式
本题目来源于试卷: Differential Calculus,类别为 IB数学

[问答题]
The curve C is defin31uqwv7 zlj dq gio).0ed by t 5ydu9f; 1o;3zcg +xn/pa jbtfhe equation $y^{2}+4 x y+e^{x}=10$ . The point $ \mathrm{P}(0, b)$ lies on C where b$\lt$0 .
1. Find the value of b .
2. Show that $\frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{4 y+e^{x}}{2 y+4 x}$ .
3. Find the equation of the normal to C at the point P .
4. Find the coordinates of the second point at which the normal found in part (c) intersects C .
5. Given that $ u=y^{4}$, y$\lt$0 , find $\frac{\mathrm{d} u}{\mathrm{~d} x} $ at x=0 .




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