\(\lim\limits_{x\rightarrow3}f\left(x\right)=\lim\limits_{x\rightarrow3}\dfrac{\sqrt{x^2+7}-4}{2x-6}=\lim\limits_{x\rightarrow3}\dfrac{x^2-9}{2\left(x-3\right)\left(\sqrt{x^2+7}+4\right)}\)
\(=\lim\limits_{x\rightarrow3}\dfrac{\left(x-3\right)\left(x+3\right)}{2\left(x-3\right)\left(\sqrt{x^2+7}+4\right)}=\lim\limits_{x\rightarrow3}\dfrac{x+3}{2\left(\sqrt{x^2+7}+4\right)}\)
\(=\dfrac{6}{2\left(4+4\right)}=\dfrac{3}{8}\)
\(f\left(3\right)=1-2m\)
Hàm liên tục trên R khi:
\(1-2m=\dfrac{3}{8}\Rightarrow m=\dfrac{5}{16}\in\left(0;1\right)\)
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