Memo Clock

Memo Clock

Turn formulas, concepts and worked problems into cards, and see each one again right when it is due.

Tangent plane

Write the tangent plane to a surface. How do you find the normal?

z−z0=fx(x0,y0)(x−x0)+fy(x0,y0)(y−y0)z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)
z−z0=fx(x0,y0)(x−x0)+fy(x0,y0)(y−y0)\begin{aligned}z-z_0&=f_x(x_0,y_0)(x-x_0)\\&\quad+f_y(x_0,y_0)(y-y_0)\end{aligned}
z=f(x,y)z=f(x,y)surface (x0,y0,z0)(x_0,y_0,z_0)point of tangency fx, fyf_x,\ f_ypartial derivatives

For an explicit surface z=f(x,y)z=f(x,y); a normal vector is (−fx, −fy, 1)(-f_x,\,-f_y,\,1).

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4:20 pmTangent planeCalculusz−z0=fx(x−x0)+fy(y−y0)z-z_0=f_x(x-x_0)+f_y(y-y_0)
Tmrw 09:30L’Hôpital’s ruleCalculuslim⁡f(x)g(x)=lim⁡f′(x)g′(x)\lim\frac{f(x)}{g(x)}=\lim\frac{f'(x)}{g'(x)}
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Lagrange multipliers∇f=λ∇g\nabla f=\lambda\nabla g
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