Apply Limit Laws, when appropriate, to quickly compute limits (ex: rational functions when denominator is nonzero)
Apply the Squeeze Theorem (aka Sandwich Theorem) to compute limits
Apply algebraic techniques to compute limits
Video1.3.1.Limit Laws.
This video introduces several Limit Laws, their intuition, and why we have to carefully check the conditions of the laws.
Post-video reflection.
The formulas alone in the Limit Laws in the video aren’t ALWAYS true. What are the important condition(s) to check for them to apply?
Video1.3.2.Limits of Rational Functions.
This video applies the Limit Laws of video 1 to deduce how to quickly compute the limit of a rational function when the denominator is nonzero.
Post-video reflection.
For a rational function, what is the key thing to check before we just "plug the value in" and say that \(\displaystyle\lim_{x\to a}f(x)=f(a)\text{?}\)
Video1.3.3.Four Algebraic Tricks for computing Limits.
This video combines multiple algebraic tricks into one. In class we covered the four basic tricks, and if you need a refresher first then watch this one first: 2.2 Part IV: Four algebraic techniques to compute limits
Video1.3.4.A trickier example of computing limits algebraically.
This video combines multiple algebraic tricks into one.
Post-video reflection.
When can you just "plug in" the value you are taking the limit towards, and when do you have to apply an algebraic trick? What features in the expression would you use to decide which algebraic trick might apply?
