Sunday, November 13, 2011
Anybody can help me with Intermediate Value Theorem problems plz??
The IVT basically is just common sense. Take the third question for instance. uming the room the oven in is less than 250� (which it should be because otherwise you'd be boiling and dead) then once the power is cut from the heating coil it has to cool to at least the temperature of the room (uming the ambient temperature (the temperature surrounding the oven) is less than 170�, which again it should be or else you'd be pretty much dead) it will have to, at some point, be that temperature before reaching the temperature of the room. More specifically this MUST be the case because the function governing cooling is continuous. Like if you take ice out of the freezer it doesn't just instantly turn to water, it takes time (even if you drop it into lava it still takes time to warm (opposite of cool)). Anyway, for the first since it goes from negative to positive, and the function is continuous at least on the interval, it must at some point on the interval cross the x-axis an therefore equal zero. You can estimate this point using Newton's theorem or any other approximation method, but because the function is a smooth curve you can guess that the zero is at about 1.5. The second works the same as the first.
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