→ dachun:哦 原來只是方向導數 01/12 00:03
※ 引述《dachun (大)》之銘言：
: → → →
: ▽T=(8x-3y+2yz)i+(-3x+2xz)j+(2xy)k (梯度)
: → → →
: 1. ▽T(3,4,5)=52i+21j+24k
: ___________________
: 2.|▽T(3,4,5)|=√52^2 + 21^2 + 24^2 = 61
: 第3小題我不確定題意請高人再指點@@
: ※ 引述《Wei2008 (Wei)》之銘言：
: : Over a certain space the temperature is given by T(x,y,z)=4x^2+3xy+2xyz
: : 1. In which direction does the temperature change most rapidly
: : at point P(3,4,5)?
: : 2. What is the maximum rate of change at point P?
: : 3. What is the rate of change at point P in the direction of vector
: : 向量v = 向量i +向量j -向量k
: : 謝謝~~~
將v化為單位向量u=(1,1,-1)/√3
DuT= ▽T˙u = 〔52×1＋21×1＋24×(-1)〕/√3
=49/√3
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