11/11/2022 0 Comments Non zero over zero limits![]() ![]() This is a one minus cosine squared theta, so it's not completely obvious yet of how you can simplify it, until you realize that This is equal to one minus cosine theta over two times one minusĬosine squared theta. That sine squared theta plus cosine squared theta is equal to one or, we know that sine squared theta is one minus cosine squared theta. Straight out of the unit circle definition of sine and cosine. ![]() Pythagorean, Pythagorean Identity in Trigonometry, it comes And the one that jumps out at me is that we have the sine squared of theta and we know from the Some trig functions here, so maybe we can use some Rewrite it in some way that at least the limitĪs theta approaches zero isn't going to, we're One minus cosine theta over two sine squared theta, and let's see if we can Let's say that this right over here is F of X. So if we said, so let's just say that this, let me use some other colors here. But let's see what we canĭo to maybe, to maybe think about this expression in a different way. Limit doesn't exist and you would say, well you Number divided by zero, then you say, okay that It just means, well maybe there's some otherĪpproaches here to work on. And once again, this indeterminate form when you have zero over zero,ĭoesn't mean to give up, it doesn't mean that You multiply times two, you still got zero. Zero, and you square it, You still got zero and Then one minus one is zero, and sine of zero is To one minus cosine of zero over two sine squared of zero. To be the same thing, as just evaluating themĪt theta equals zero So this is going to be equal They'd be continuous at theta equals zero, so the limit is going "of theta, as theta approaches zero, "over the limit, "as theta approaches zero "of two sine squared theta." Now, both of these expressions which could be used to define a function, that they'd be continuous Temptation is to say, "Well, this is going to be the same thing "as the limit of one minus cosine theta "as X approaches, or not X, "as theta approaches zero. The video and see if you could work through this. Of one minus cosine theta over two sine squared theta. If we can find the limit as theta approaches zero ![]()
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