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Unformatted text preview: z = e 3 x +2 y , y = ln(3 u-w ) , x = u + 2 v. Calculate ∂z ∂v , ∂z ∂w . Problem 7. Find the point on the plane 2 x + 3 y + 4 z = 29 that is closest to the origin. 1 Problem 8. Calculate the derivative of the function f : U → Mat n × n , A → ( I + A 2 )-2 deﬁned on the open subset where I + A 2 is invertible. Problem 9. Show that the function f ( x,y ) = ( x 3 x 2 + y 2 if ( x,y ) 6 = (0 , 0) if ( x,y ) = (0 , 0) admits all directional derivatives, it is continuous but it is not diﬀerentiable. Problem 10. Show that a diﬀerentiable function f : R n → R m is continuous. Problem 11. Find the minimal distance between two points on the ellipse x 2 + 3 y 2 = 9 and the circle x 2 + y 2 = 1....
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This note was uploaded on 03/28/2011 for the course MATH 31B taught by Professor Dragosoprea during the Winter '11 term at UCSD.
- Winter '11
- Critical Point