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### 26 Cards in this Set

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 linearization of f at (a,b) L(x,y)= f(a,b)+ fx(a,b)(x-a)+fy(a,b)(y-b) to convert from rectangular to spherical 1. p^2=x^2+y^2+z^2 2. pcos(fi) 3. x=psin(fi)cos(theta) 4. y=psin(fi)sin(theta) formula for scalar projection of b onto a a*b ____ lal formula for vector projection of b onto a a*b ____ lal^2 what does cross product do if axb = 0 // laxbl = area of the parallelogram finds normal vector to both vectors a and b cylindrical coordinates P( , , ) P(r,theta,z) laxbl when theta is the angle btwn two vectors laxbl= lallblsin(theta) equation of tangent plane to surface z=f(x,y) at P(x0,y0,z0) z-z0=fx(x0,y0)(x-x0)+fy(x0,y0)(y-y0) z=f(x,y) dz=.... dz=fx(x,y)dx +fy(x,y)dy =dz dz ---- dx + ---- dy dx dy formulas for vector equations and parametric equations vectors parametric x=x0+at y=y0+bt z=z0+ct // to vector what is the relationship btwn position, velocity, and acceleration? pos: r(t) vel: r'(t) acc: r''(t) = v'(t) arc lenth formula integral from a to b of the magnitude of r'(t) Sa,b l r'(t)l dt to convert from rectantular to cylindrical r^2=x^2+y^2 tan(theta)=y/x z=z x=rcos(theta) y=rsin(theta) how do you find the dot product what happens if it =0 a(a,b,c) b(d,e,f) a*b=ad+be+cf their orthagonal unit vector a --- lal spherical coordinates P( , , ) P(p,theta,fi) to convert from spherical to rectangular x=psin(fi)cos(theta) y=psin(fi)sin(theta) z=pcos(fi) curvature of a curve k= l T'(t) l ------- l r'(t) l T(t) T(t)= r'(t) ----- l r'(t) l linear appx of f(x,y) at (a,b) aka tangent plane appx f(x,y)= f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b) -x^2 - y^2 + z^2 ---- ----- ---- = 1 a^2 b^2 c^2 hyperbaloid of 2 sheets z x^2 + y^2 --- = ---- ---- c a^2 b^2 elliptic paraboloid z^2 x^2 + y^2 ---- = ----- ----- c^2 a^2 b^2 cone z x^2 - y^2 --- = ----- ---- c a^2 b^2 hyperbolic paraboloid x^2 y^2 z^2 ---- + ---- + ----- = 1 a^2 b^2 c^2 ellipsoid x^2 y^2 - z^2 ----- + --- ---- =1 a^2 b^2 c^2 hyperbaloid of 1 sheet