Investigating Limits: What Happens When x Approaches a Constant or Zero?

Thread starter nycmathguy
Start date Jun 17, 2021

Click For Summary

The discussion focuses on investigating limits as x approaches specific values, specifically 3 and 0. Participants are encouraged to analyze the limits of the function f(x) at these points. There is a suggestion that understanding one limit will aid in comprehending the other. The thread is closed due to its similarity to a previous discussion. Overall, the emphasis is on the importance of limit evaluation in calculus.

Jun 17, 2021

nycmathguy

Homework Statement: Investigate each limit.

Relevant Equations: See attachment of piecewise function.

Investigate each limit.

1. lim f(x) x→3

2. lim f(x) x→0

See attachment.

Physics news on Phys.org

Jun 17, 2021

Mark44

Mentor

Insights Author

Thread closed. This is nearly identical to your other thread with almost the same name. When you figure this one out, you'll be able to figure this one out.

Thread 'Does this series converge uniformly?'

First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...

View full post »