test 2

test 2 - Steepest descent =-|▼F| When a hiker has no...

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Type I Limits If lim(0,0) = 0/0 check lim(0,y,) = lim(x,0) If lim(0,y) = lim(x,0) = 0/0 check lim(x,x,) = lim(y,y) If lim(x,x) = lim(y,y) = 0/0 check lim(x,x^2) = lim(y,y^2) If the limits do not equal the function is discontinuous Use the squeeze theorem when you see two variables Multiplied on the top but added on the bottom To find if a function is continuous find the domain of g(x,y) Type II Sin -> cos -> -sin -> -cos d^2z/drdθ = d/dr(dz/dx) = d/dx dz/dx dx/dr + d/dy dz/dx dy/dr v= dv/dt= ∏(dh/dt dt/dh + dr/dt dt/dr) Type III z-zo =fx(xo,yo)(x-xo) + fy(xo,yo)(y-yo) fx = dz/dx = -df/dx / df/dz fy = -df/dy / df/dz if fx or fy is undefined change the format to x-xo or y-yo Finding the normal: use the coefficients to find the normal vector equation <xo,yo,zo> + t<coefficients> Tangent plane parallel to another plane: Solve for tangent equation set normals <fx,fy,z> = K<normal to the equation> solve for x,y,z Type IV Directional derivative: ▼F - |n| n = direction vector To find the steepest slope: |▼F| = (fx(xo,yo)^2 + fy(xo,yo)^2)^1/2
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Unformatted text preview: Steepest descent = -|▼F| When a hiker has no slope find vector perp. To |▼F| by <-fx,fy,0> Points parallel to a plane: Solve for ▼F set = K<np> solve for K, use K to solve for x,y,z Type V Solving for critical points. Fx = 0 fy = 0 and fx = fy Second derivative test: d = fxx(fyy) –(fxy)^2 When fxx is negative, and d is positive = loc. Max When fxx is positive and d is positive = local min When fxx, is either, and d is negative = saddle point To find the values plug the critical point in to f(x,y) When finding equation point closest to another point, set D^2 = (x + a)^2 + (y+b)^2 + (z+c)^2 where (a,b,c) = the point ▼F=▼G K solve for (x,y,z) by solving for K and plugging it into the ▼G K VI Find the critical points, and the extremes test by plugging into ▼F, greatest value = max smallest = min Type VII Solve for xyz using ▼F = ▼G K Take the xyz and f\plug them into ▼F to solve for abs min amd max...
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This note was uploaded on 07/19/2010 for the course EK 211 taught by Professor Attaway during the Spring '10 term at BU.

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