Compute limits at infinity for various transcendental functions (ex. \(e^x\) and \(\arctan(x)\)).
Compute limits at infinity for rational functions.
Video1.6.1.Infinite Limits.
In this video we discuss limits at infinity for the function \(\arctan(x)\) and \(e^x\text{.}\) We are both learning about limits at infinity as well as building our familiarity with these two important functions in calculus.
Post-video reflection.
Describe in words what it means for a limit to be infinite.
Video1.6.2.Limits at Infinity.
In this video we discuss limits at infinity for the function \(\arctan(x)\) and \(e^x\text{.}\) We are both learning about limits at infinity as well as building our familiarity with these two important functions in calculus.
Post-video reflection.
In this video we talked about expressions like \(\displaystyle\lim_{x\to\infty}f(x)=L\) and in contrast, in class you might have seen \(\displaystyle\lim_{x\to a}f(x)=\infty\text{.}\) What is the difference between these two concepts?
Video1.6.3.Limits at Infinity for Rational Functions.
For many functions f(x) such as the rational function we see in this video, we can use some algebra to determine the value of the limit at infinity.
Post-video reflection.
For a rational function, what is the key thing to check before we just "plug the value in" and say that \(\displaystyle\lim_{x\to a}f(x)=f(a)\text{?}\)
