211exam2-f08 - where.x tz 1 y b)Evaluateffatu:2,v:1 for...

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\ . - MATH 2ll- EXAM II - OCTOBER 29,2008 1) a)Find all local minima, maxima, and saddle points (if they exist) for z : 6x2 -2x3 +3y2 +6xy b)Determine if the limit exists(show all work) lim t*'f, (xY)'(0,0) x"Y+xY' 2)Consider the surface described implicitly by the equation 2yf +( * xzlny : J a) Find the equation of the tangent plane to the surface at the point (1,1,1) b) Using the linear approximation evaluate the approximate value of z on the surface when x:l.01 and y:.98 3)Using the chain rule a)nvaluate ft att:1 for z: xTe(zrr)
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Unformatted text preview: where .x: tz +1, y - + b)Evaluateffatu:2,v:1 for w:xlz+y2+z2where x: Lt*v, l: ttv, r: # 4)For the functionJ(x,,y) : (?.x - 3y + 4z)3 at the point P(-5,1,3) a) Determine the directional derivative in the direction V : i - k b) Determine a unit vector in the direction where the function changes most rapidly 5)Using Lagrange multipliers find the highest and lowest temperature on the surface of the sphere, x2 + y2 + z2 : I where the temperature distribution within the sphere is described by T - 40,0xy22...
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