Limits of Function with complex numbers

**zebra2147** · October 17th 2010, 04:15 PM

I am studying for an exam and came across this excercise...
Let $f: D\rightarrow C$
(complex numbers). Suppose a is a limit point of D. If $f(x)\rightarrow b$ as $x\rightarrow a$ , then $Re(f(x))\rightarrow Re(b)$ as $x\rightarrow a$ .

So we have that if $0<|x-a|<\delta \Longrightarrow |f(x)-b|<\epsilon$ ,
then, $0<|x-a|<\delta \Longrightarrow |Re(f(x)-Re(b)|<\epsilon$ .
However, I'm not sure how to use this to find the apropriate values for epsilon and delta that makes this true. Any help would be appreciated.

**Plato** · October 17th 2010, 04:58 PM

You have post some serious problems.
http://www.mathhelpforum.com/math-he...ial-19060.html
So Why not learn to post in symbols? You can use LaTeX tags.
You are more likely to receive serious attention if your posting are easy to read.

**zebra2147** · October 17th 2010, 05:43 PM

I am studying for an exam and came across this excercise...
Let $f: D\rightarrow C$
(complex numbers). Suppose a is a limit point of D. If $f(x)\rightarrow b$ as $x\rightarrow a$ , then $Re(f(x))\rightarrow Re(b)$ as $x\rightarrow a$ .

So we have that if $0<|x-a|<\delta \Longrightarrow |f(x)-b|<\epsilon$ ,
then, $0<|x-a|<\delta \Longrightarrow |Re(f(x)-Re(b)|<\epsilon$ .
However, I'm not sure how to use this to find the apropriate values for epsilon and delta that makes this true. Any help would be appreciated.

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