# Thread:

1. ## Continuity of  1/x

Show that 1/x is continuous on at any c =/= 0
hint: chose delta to stay away from 0

i have a general idea of how it works but I'm not really sure how to
"use delta = min{[c]/2,c^2(e/2)} "(answer from book)

2. Originally Posted by mtlchris
Show that 1/x is continuous on at any c =/= 0
hint: chose delta to stay away from 0

i have a general idea of how it works but I'm not really sure how to
"use delta = min{[c]/2,c^2(e/2)} "(answer from book)
Did you try writing out the definition?

$\left|\frac{1}{x}-\frac{1}{c}\right|=\left|\frac{c-x}{xc}\right|$....how look that the $\delta$. It's $\min$ because obviously we want to restrict our attention so that we may apply some estimation (i.e. on "whatever" neighborhood of c it is always true that "whatever" is less than or equal to "whatever else"). Also, use that in conjunction with the fact that you really only care about bounding $\frac{1}{|xc|}$ for one can make $|c-x|$ as arbitrarily small as one wants.
{"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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": false, "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": 0.9652602076530457, "perplexity_flag": "middle"}