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Evaluate Fractions
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Show that Let f : \mathbb{R} \setminus \{0\} \to \mathbb{R} be defined by f(x) = \frac{1}{x}. Show \lim_{x \to 0}\frac{1}{x} doesn't exist.
https://math.stackexchange.com/q/2826102
Suppose that f: U → R is an application defined on a subset U of the set R of reals. If p is a real, not necessarily belonging to U but such that f is "defined in the neighborhood of p", ...
Find \lim_{x\rightarrow0}\frac{x}{[x]}
https://math.stackexchange.com/q/2835948
For x\to 0 the expression \frac{x}{[x]} is not well defined since for 0<x<1 it corresponds to \frac x 0 and thus we can't calculate the limit for that expression. As you noticed, we can only ...
Disprove the limit \lim_{x\to 0}\frac{1}{x}=5 with epsilon-delta
https://math.stackexchange.com/q/1527181
Given \epsilon> 0, we want to find \delta> 0 such that if |x- 0|= |x|< |\delta| then |\frac{1}{x}- 5|< \epsilon. Of course, |\frac{1}{x}- 5|= |\frac{1- 5x}{x}| so, if x is positive, |\frac{1}{x}- 5|<\epsilon ...
Is this a valid use of l'Hospital's Rule? Can it be used recursively?
https://math.stackexchange.com/questions/946785/is-this-a-valid-use-of-lhospitals-rule-can-it-be-used-recursively
L'Hôpital's Rule Assuming that the following conditions are true: f(x) and g(x) must be differentiable \frac{d}{dx}g(x)\neq 0 \lim\limits_{x\to c} \frac{f(x)}{g(x)}= \frac{0}{0}\mbox{ or }\lim\limits_{x\to c} \frac{f(x)}{g(x)}= \frac{\pm\infty}{\pm\infty} ...
How to explain that division by 0 yields infinity to a 2nd grader
https://math.stackexchange.com/questions/242258/how-to-explain-that-division-by-0-yields-infinity-to-a-2nd-grader
The first thing to point out is that division by zero is not defined! You cannot divide by zero. Consider the number 1/x where x is a negative number. You will find that 1/x is negative for all ...
precise definition of a limit at infinity, application for limit at sin(x)
https://math.stackexchange.com/questions/1776133/precise-definition-of-a-limit-at-infinity-application-for-limit-at-sinx
Some items have been dealt with in comments, so we look only at c). We want to show that for any \epsilon\gt 0, there is a B such that if x\gt B then |\sin(1/x)-0|\lt \epsilon. Let \epsilon\gt 0 ...
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\lim_{ x \rightarrow 0 } 5
\lim_{ x \rightarrow 0 } 5x
\lim_{ x \rightarrow 0 } \frac{2}{x}
\lim_{ x \rightarrow 0 } \frac{1}{x^2}
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