Linear approximation
L(x,y)=f(x0,y0)+fx(x0,y0)(x−x0)+fy(x0,y0)
(y−y0)
Tangent
fx(x0)(x−x0)+fy(y0)(y−y0)−fz(z0)(z−z0)=0
normal line
r(t)=⟨x0,y0,z0⟩+t∇f(x0,y0,z0)
Directional derivative
D→uf(x,y,z)=fx(x,y,z)a+fy(x,y,z)b+fz(x,y,z)c
to
u
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equation sheet for calculus 3.
Typology: Cheat Sheet
2024/2025
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Linear approximation L(x,y)=f(x0,y0)+fx(x0,y0)(x−x0)+fy(x0,y0) (y−y0) Tangent fx(x0)(x−x0)+fy(y0)(y−y0)−fz(z0)(z−z0)= normal line r(t)=⟨x0,y0,z0⟩+t∇f(x0,y0,z0) Directional derivative D→uf(x,y,z)=fx(x,y,z)a+fy(x,y,z)b+fz(x,y,z)c