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OpenStudy (anonymous):
Determine the function and is it continuous at (0,1)? This is what I did but I'm sure it's wrong. \[f(x,y)=(x+1)y \div1-x-y \] \[=xy+y \div 1-x-y\] \[\lim_{(x,y) \rightarrow (0,1)} xy+y \div 1-x-y\] \[=\lim_{(x,y) \rightarrow (0,1)} xy+y \div \lim_{(x,y) \rightarrow (0,1)} 1-x-y\] \[=(\lim_{(x,y) \rightarrow (0,1)} x \times \lim_{(x,y) \rightarrow (0,1)} y + \lim_{(x,y) \rightarrow (0,1)} y) \div (1 \times \lim_{(x,y) \rightarrow (0,1)} -x -\lim_{(x,y) \rightarrow (0,1)} -y)\] \[=xy+y \div 1(-x-y)\] \[=xy+y \div -x-y\] At the point (0,1): \[=0 \times 1 + 1 \div -0 -1\] \[=1 \div -1 = -1\]
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OpenStudy (anonymous):
The proper question is "For the given function determine the limit at the given point and is the function continuous at the given point?
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