Re: [微分] 切線斜率--極座標
※ 引述《ht15trep (柏林=Boring)》之銘言：
: r = 4sin3θ
: slope of tangent line at θ=π/4 is ??
: 請問這要怎麼算= =??
: ans: 1/2
x = rcosθ = (4)(sin3θ)(cosθ)
y = rsinθ = (4)(sin3θ)(sinθ)
dy |
----|
dx |θ=π/4
dy/dθ|
= -------|
dx/dθ|θ=π/4
(12)(cos3θ)(sinθ) + (4)(sin3θ)(cosθ)|
= ----------------------------------------|
(12)(cos3θ)(sinθ) - (4)(sin3θ)(sinθ)|θ=π/4
-1 1 1 1
(12)(----)(----) + (4)(----)(----)
√2 √2 √2 √2
= ---------------------------------------
-1 1 1 1
(12)(----)(----) - (4)(----)(----)
√2 √2 √2 √2
(12)*(-1/2) + (4)*(1/2)
= --------------------------
(12)*(-1/2) - (4)*(1/2)
-6 + 2 -4 1
= --------- = ---- = ---
-6 - 2 -8 2
--
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07/05 16:13, , 1F
07/05 16:13, 1F
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