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 Sep29 awarded Popular Question Sep20 comment Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ @AndréNicolas I see now. Thanks. By the way, you picked $\frac{1}{4}$ because it made arithmetic easier - but how can I determine the "largest acceptable value" that can replace $\frac{1}{4}$? (out of curiosity) Sep20 accepted Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ Sep20 comment Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ @EWHLee I see. I wonder if $\frac{1}{4x-9}$ should have been $\frac{1}{|4x-9|}$ instead... Wait, no, that doesn't work either. Goddammit. What should I have done instead? Sep20 comment Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ @AndréNicolas Ahhhh yes, that's right. By the way, isn't $|(x-3)| < \delta < \frac{9}{4}$ enough to keep $|4x-9|$ away from $0$ since $\frac{9}{4}$ is the solution to $4x-9$? Sep20 asked Proving that $\lim_{x\to3}\frac{x}{4x-9}=1$ Sep20 asked Why is $|(x-2)| < \delta \le 1$ true when proving $\lim_{x\to2}(3x^2-x)=10$? Sep19 comment Proving $\lim_{x\to1}(x^2+3)=4$ Hm I'm not very sure how can $|x-1| < \delta$ lead to $|x+1|\le 3$. If you increase $|x-1|$ by $2$ to reach $|x+1|$, shouldn't it be $|x+1| \le 2$ rather than $3$? Sep19 accepted Proving $\lim_{x\to1}(x^2+3)=4$ Sep19 comment Why does $|x-1|^2+3|x-1| < \epsilon \implies |x-1|^2 < \frac{\epsilon}{2} \ \ \land \ \ 3|x-1| < \frac{\epsilon}{2}$? @Oleg567: What if $a = b = \epsilon/2$? Sep19 asked Why does $|x-1|^2+3|x-1| < \epsilon \implies |x-1|^2 < \frac{\epsilon}{2} \ \ \land \ \ 3|x-1| < \frac{\epsilon}{2}$? Sep19 asked Proving $\lim_{x\to1}(x^2+3)=4$ Sep12 asked Determinant of a matrix with trigonometry functions. Sep7 asked Determining what values in a system can cause infinite/unique/no solutions. Sep7 comment For what values of $p$ and $b$ is the vector $(b,8,b+7)$ a solution of this system? Thanks, that's right (although $b$ yields $-5$). Sep7 accepted For what values of $p$ and $b$ is the vector $(b,8,b+7)$ a solution of this system? Sep7 comment For what values of $p$ and $b$ is the vector $(b,8,b+7)$ a solution of this system? @Adriano: Huh, it seems it should be $b = -5$. The exercise's answer seems to be wrong haha. Sep7 revised For what values of $p$ and $b$ is the vector $(b,8,b+7)$ a solution of this system? added 1 character in body Sep7 asked For what values of $p$ and $b$ is the vector $(b,8,b+7)$ a solution of this system? Sep5 accepted Determining the values of $b$ in $Ax=b$ to have a consistent system.