Suppose that $f$ and $g$ are both functions from $R^k$ to $R^m$, which are continuous at $x\in R^k$. Suppose that $g(x)\neq 0$. Prove that the quotient function $f/g$ is defined and continuous at $x$.
Continuity of a quotient function
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functions
continuity
1 Answers
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Since $g(x)\ne 0$, there is a neighborhood of $x$ where $|g(z)|>|g(x)|/2$.
Use this and the continuity of $f$