It's also one of my favorite topics because I get to use my "spit in the ocean" phrase. When we talk about limits of f(x) as x approaches infinity, and I tell them to only look at the highest powered terms in each of the numerator and denominator, and we test examples on the graphing calculator ...... I describe the largest term like the ocean and everything else as spit. The spit does not change the volume of the ocean significantly.
And without fail, every year someone brings up "Mean Girls".
The "plug in a number" rule only works for continuous functions. It is, in fact, the definition of continuity.
ReplyDeleteHi GSWP,
ReplyDeleteI agree with you that you can only evaluate a continuous function by plugging in a number. However, by plugging in a number into any rational function that you are trying to find the limit of, this step is a clue to what may be happening at/around that point and what you may have to do next to make your limit decision.
Have to borrow "spit in the ocean," it's almost visual!
ReplyDeleteI had a day last spring when (after talking about limits for a few days in precalc) my juniors were out for a class and I was only left with a few seniors. They talked me into watching Mean Girls in class.... yeah, won't repeat that again! I'd forgotten some of the language that was in it. Lesson learned! :)
ReplyDeleteOy! It was probably like watching "sex" scenes with your parents in the room .... or was it just like, "la la la la. Pretend you don't hear the potty mouths, children."
ReplyDeleteI love this chart so much! I'm stealing it for when I teach Calc I this summer. :) For the types of functions beginning pre-calc/calc students encounter, I think the chart works so nicely. Going from finding limits graphically to algebraically can be quite a challenge sometimes. It's so intuitive graphically...and then it's not so intuitive algebraically. What do you think about adding graphs to each of the examples? I wonder if that would add or take away from the great thing you have going on here.
ReplyDeleteI'm glad you like it. I'm hoping the kids refer back to it and see the whole picture eventually.
ReplyDeleteGraphs .... I don't know, it could work, but I don't have a vision of it. When I do the graph limits, I talk a lot about "what y intends to do" ... and ... "it's not what y actually does, but what it LOOKS like it's going to do." We also talk about moving our chubby fingers along the path and see where we seem like we're intending to end up. I think that works ... I'll have to check back with my kiddies after our week-long state testing absence of class.
Have fun with calculus this summer.