I had an awful day yesterday in my calculus class. I began teaching the new lesson, then I just completely forgot what I was saying, so I started over from the beginning. Then when I introduced a formula, the linearization function, L(x) = f(a) + f'(a)(x - a), I wrote a minus sign instead of a plus sign in the function, completely changing what I was supposed to do. As if that weren't bad enough, I then made not one, but two simple algebraic errors which of course kept me from showing that the equation did what I told my students it would do. Oh, and at the very end of class, when giving another equation, I said that x could not equal zero when I meant to say that it had to be close to zero. Hopefully I didn't mess any of my students up too much. Wish me luck. Today I get to repair all of the damage I did yesterday.
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