The predefined definition in the app is the [math]\left(\varepsilon-N\right)[/math] .[br]The button at the bottom right of the app allows you to toggle between this definition and the definition based on neighborhoods.[br][br]Explore the definition step by step, then use the slider to modify the intervals on the[i] y[/i]-axis and drag point [math]x[/math]to view the values of [math]f\left(x\right)[/math] in the interval in which the limit holds.
What is line [math]y=\ell[/math] for the function?
Apply the definition and state which of the following limits are correct:[br][br][math]\displaystyle{\lim_{x \to + \infty} \left( \frac{1}{3} \right) ^{x+2} = 0}[/math][br][br][math]\displaystyle{\lim_{x \to + \infty} \frac{2}{3-x^2} = 0}[/math][br][br][math]\displaystyle{\lim_{x \to + \infty} \frac{2x+3}{x+1} = 3}[/math]