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$\lim_{x\rightarrow a}(h\circ g)(x)=M$.

(Someone told me that this statement is false and should replace "$U\setminus \left \{ L \right \}$" with "$U$", and “$M=\lim_{y\rightarrow L}h(y)$. Then”

with “$h$ is continuous at $L$, then”.)

So can you give me a counterexample of the original statement? Thanks.