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- Thread starter Cbarker1
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Of course $ \frac{1}{bc} \ne \frac{b}{c}$. I'm missing something or the property is false (or they meant something else).

This is not true.I read a textbook about limits.

I saw several properties about the limits.

\(\displaystyle \lim_{x\to c} f(bx)\:=\: b\cdot\lim_{x\to c}f(x)\)

Let [tex]f(x) \:=\:2x+7[/tex]

Then: .[tex]\lim_{x\to1}f(3x) \:=\:\lim_{x\to1}(6x+7) \:=\:13[/tex]

But: .[tex]3\cdot\lim_{x\to1}f(x) \:=\:3\cdot\lim_{x\to1}(2x+7) \:=\:3\cdot 9 \:=\:27[/tex]

Perhaps you misread the identity.

The following is true.

. . [tex]\lim_{x\to c}b\!\cdot\!\!f(x) \;=\;b\!\cdot\!\lim_{x\to c}f(x)[/tex]