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Give an Appropriate Answer f(x,y,z)f ( x , y , z )

Question 204

Essay

Give an appropriate answer.
-Given the function f(x,y,z)f ( x , y , z ) and the positive number ε\varepsilon as in the formal definition of a limit, find a positive number δ\delta as in the definition that insures f(x,y,z)f(0,0,0)<ε| f ( x , y , z ) - f ( 0,0,0 ) | < \varepsilon .
f(x,y,z)=x2+y2+z2x+1;ε=0.03f ( x , y , z ) = \frac { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } { x + 1 } ; \varepsilon = 0.03

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