Quod Erat Demonstrandum

2019/05/10

線長乘積

Filed under: Pure Mathematics — johnmayhk @ 11:52 下午
Tags: ,

考慮單位圓內接正多邊形,比如正方形

由某點(比方說 A)出發,連起其他頂點,得出 3 條線段,其長度分別為 2, \sqrt{2}, \sqrt{2},故乘積(product)為 4。

對於五邊形

由某點出發連起其他頂點,得出 4 條線段,那麼線段長度的乘積如何? (more…)

廣告

2019/05/05

What’s wrong?

Filed under: Additional / Applied Mathematics,NSS — johnmayhk @ 7:05 下午
Tags: ,

Here is a basic level M2 question:

Given that \sqrt{xy}=7+2y, find \frac{dy}{dx} at (-\frac{1}{3},-3).

Student 1 gave

\frac{1}{2\sqrt{xy}}(x\frac{dy}{dx}+y)=2\frac{dy}{dx}

\frac{1}{2}\sqrt{\frac{x}{y}}\frac{dy}{dx}+\frac{1}{2}\sqrt{\frac{y}{x}}=2\frac{dy}{dx}

\frac{dy}{dx}=\sqrt{\frac{y}{x}}\cdot\frac{1}{4-\sqrt{\frac{x}{y}}}

Thus, at (-\frac{1}{3},-3),

\frac{dy}{dx}=\sqrt{\frac{-3}{-1/3}}\cdot\frac{1}{4-\sqrt{\frac{-1/3}{-3}}}=\frac{9}{11}

Student 2 gave (more…)

在WordPress.com寫網誌.