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A simple example would be $x/x$. Clearly the $x's$ just cancel out and we are left with $1$, so is the limit for $x \rightarrow whatever$ always 1?

Or, more generally, is the limit of $f(z)$ as $x \rightarrow a$ just $f(z)$?

Not sure what to do.

Daniel
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  • yes, just think to the graphic of such a function.. It's constant in $x$ – Exodd Oct 04 '14 at 14:20
  • It certainly does not depend on $x$, $x$ is just a variable. it may or may not depend on that you call $whatever$, depending on whether the function is continuous or not. By the same token the answer to your second question is no. – Git Gud Oct 04 '14 at 14:24
  • The "whatever" is just a number,0 for example, not a variable. What then? – Daniel Oct 04 '14 at 14:27

1 Answers1

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Note that $f(z)$ can factored out as a constant because $f(z)$ does not depend on $x$. Therefore, $$ \lim_{x\to a} f(z)=f(z)\left[\lim_{x\to a} 1\right]=f(z) $$

k170
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