Fall+Week+04

toc =Monday 9/7= Labor Day Weekend. Not in school. =Tuesday 9/8= Homework for tomorrow: Page 50 #4-7, 11-23 odd, 33-41 odd. In this lesson we defined a continuous function at a specific point. We also sketched graphs of Continuous functions, Removable Discontinuity, Essential Discontinuity, and Jump Discontinuity. Removable Discontinuity has a limit as x->c, x->c+, and x->c-. Essential Discontinuity's limit as x->c does not exist, and the limit as x->c+or- goes to +/- infinity. Jump Discontinuity's limit as x->c does not exist either, but has a limit as x->c+ and x->c-. We also continued to practice more difficult trigonometry limits. And it's important to remember our two identities:
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=Wednesday 9/9= media type="custom" key="4344531"

In class today we reviewed derivatives of trig functions such as: sin2x = 2sinxcosx; (1-cosx)/x = 0; sinx/x = 1

Note sin2x is not = to 2sinx (algebra makes us do it the hard way)

We also expanded on when a function is discontinous and limits of functions, even if the function does not have a steady value as x -> infinity ex: lim (cosx)/x = 0

=Thursday 9/10= =Friday 9/11= Today we learned a property of a function when its continuous on an interval called the **Intermediate Value Theorem**, but we dont have to memorize this one!!! (mostly because its kind of common sense)

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