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Mathematics
Calculus
Finding domain when using continuity to evaluate a limit
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[QUOTE="Mark44, post: 6863018, member: 147785"] You have another mistake that I didn't notice while I was focused on your difficulties with LaTeX and confusion about the union vs. intersection of two sets. Starting with ##|x - 1| \ge \sqrt 5##, This means that ##x - 1 \le -\sqrt 5## OR ##x - 1 \ge \sqrt 5## ##\Rightarrow x \le 1 - \sqrt 5## OR ##x \ge 1 + \sqrt 5##. The second line of your work above that I quoted is incorrect because you have not correctly rewritten the inequality with an absolute value to get rid of the absolute value. Again, this is stuff that is usually presented in precalculus classes. [B]Until you get a better grip on these basics, you are going to continue to have problems with more advanced topics.[/B] The last pair of inequalities that I wrote can be written in set-builder notation like so: ##\{x | (-\infty < x \le 1 - \sqrt 5) \cup (1 + \sqrt 5 \le x < \infty)\}## or in interval notation like this: ##x \in (-\infty, 1 - \sqrt 5] \cup [1 + \sqrt 5, \infty)##. [/QUOTE]
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Mathematics
Calculus
Finding domain when using continuity to evaluate a limit
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