Thread:

1. Limits of Function with complex numbers

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.

2. 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.

3. 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.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9395637512207031, "perplexity_flag": "head"}