234-dickey-07sp02 - MATH 234 Lee 2 EXAM#2 YOUR NAME T.A's...

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Unformatted text preview: MATH 234, Lee. 2, EXAM #2 YOUR NAME T.A.'s NAME DISC. SEC. (Time and Day) Show all your work. No calculators or references. ”“"—-—l } 1.(20 points) I l l 2.(2o points) l 3.90 points) l , 4.(20 points) 5.(20 points) 1. Decide whether the following functions are continuous at . (0,0). Justify your answer. ’ (a) f(x.y)= 'JL. (mo/1’ (0,0) 2x2-fy2 o (m) =’ (0.0) (b) f(x,y) = "__y__ (m) 7310.0) Xz+xy+y2 0 (KY) =(0.0) 2. Find the equation of the plane which is'tangent to the surface 2 = sinh(x2 + y) at the point (1 ,—1 ,0). The temperature at any point in space is given by T = xy'+ yz + zx. (a) Find the direction in which the temperature increases most rapidly at the point (1,1,1) and determine the maximum rate of change at this point. (b) Find the derivative of T in the direction 3A- 412 at the point (1,1,1). 4. Find the absoiute maximUm and minimum for f(x,y) = x2 + 2y2 in the region x2 + y2 _<_ 1. 5. ' Find the maximum and minimum values for the function f(x,y,z) = x + 2y where (x,y,z) must satisfy the constraints x+y+z=1andy2+22=4. ...
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