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182E2-S1997 - (10 pts(10 pts(10 pts(10 pts MATHEMATICS 182...

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Unformatted text preview: (10 pts) (10 pts) (10 pts) (10 pts) MATHEMATICS 182 TEST 2 1) If (x,y,z) = way + z2 find (a) the gradient, Vf, at (1,1n2, §), _. 1 1 b the directional derivative of in the direction of V = — i+ — k at ( ) f (fl) (fl) (1,1112, é) . 2) If 2 is defined as a function of :1: and y by asy+z3a3—2yz= Oz find E at (1,1,1). 3) Find the tangent plane and normal line to z — $2 — y2 = 1 at (2, 2, 5). 4) If f(x,y) : y(sin:c) find (a) fmwvfmyafyy at (070) (b) the quadratic approximation of f (x, y) at (0, O). (15 pts) 5) If 2 = sin(my) + x(sin y), x=u2+v2, andyzm) find if Whenuzflandvzl. Bu (15 pts) 6) a) If f(x,y) = my2 + y(cos:1:) find the linearization [(1534) of f(ac, y) at (0,1). . . 1 1 b) Est1mate the error if |xl < T6 and |y — 1| < m. (15 pts) 7) Find the absolute maximum value and the absolute minimum value of the function f(a:,y) : $2 + my + y2 on the rectangular plots 0 g a: g 5 and —1 g y g 1. (15 pts) 8) Find the points on x + 2y + 3z = 13 closest to (1,1,1). ...
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