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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1820.0. "Continuous Functions?" by RHINOS::OVEN () Tue Dec 07 1993 09:23

    Are the following functions continuous at (0,0)? Explain, please...
    
            (sin(y))/y)*(x^2 + 1)	if y does not = 0
    f(x,y)= 
    	     1				if y = 0
    
    
    
    
             1				if x = y^2
    z(x,y) = 
    	     (x^2 + 2*x*y - x*y^2 - 2*y^3)/(x - y^2)     otherwise
    
    
    					Thanks,  Dave

T.R Title User Personal
Name Date Lines

1820.1 Yes and no HERON::BLOMBERG Trapped inside the universe Tue Dec 07 1993 12:05 14

T.R	Title	User	Personal Name	Date	Lines
1820.1	Yes and no	HERON::BLOMBERG	Trapped inside the universe	`Tue Dec 07 1993 12:05`	14
	f(x,y) = h(x,y)*g(x,y) where h(x,y) = sin(y)/y if y.ne.0, 1 if y=0 g(x,y) = 1+x^2 Both f and g are continous at (0,0), hence f too. z(x,y) = x + 2y if x.ne.y^2, 1 if x=y^2 z(0,0) = 1, but x + 2y obviously approaches zero as x and y approaches zero. Hence z is not continous at (0,0).


	f(x,y) = h(x,y)*g(x,y) where

		h(x,y) = sin(y)/y if y.ne.0, 1 if y=0
		g(x,y) = 1+x^2

	Both f and g are continous at (0,0), hence f too.


	z(x,y) = x + 2y if x.ne.y^2, 1 if x=y^2

	z(0,0) = 1, but x + 2y obviously approaches zero as x and y
	approaches zero. Hence z is not continous at (0,0).