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Make the given changes in the indicated examples of this section and then solve the resulting problems.In Example $5,$ change the denominator $1-\cos x$ to $1+\cos x$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 7

L'Hospital's Rule

Derivatives

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03:12

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Work each problem.$$\t…

01:00

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00:48

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00:42

For the following exercise…

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01:47

All right. We are re evaluating this limit. Uh It's still to sin effects in the numerator. But the denominator ah I just lost it uh goes from one minus co sign to one plus co sign. And it's the limit as X approaches pi on the Oh rats. I definitely lost. Yeah, I believe it's on the left side. So as we look at the problem, if you were to look at sign um and we're looking at the order pair negative 10 will sign. It's the Y coordinate. So when I plug in sine of pi I'm going to get zero there. So I get zero in the numerator and the denominator co sign is the X coordinate on the unit circles. One plus negative one is also zero. So we do have the indeterminant form 0/0. To use the local tiles rule. So what we do for love me towels is we take the derivative of the top and bottom. So the this limit that we have down here is going to be equal to, well the derivative of the top of me to cosign effects. And then the drift of one is zero. So I don't have to write that down. But the drift of a co sign would be negative sign. So as we're doing this uh and we go to evaluate, I should be doing arrows again because direct substitution and say I have two times zero in the numerator over a sign of that. No, I did that wrong brunch. Okay. Co sign is the excellent. So it's two times negative one and then a sign of pi zero. So when you have a constant divided by zero, what we say is that the limit does not exist. It's either infinity or negative infinity. And if I were a betting person because its a negative over a negative, we'd be looking at approaching infinity. But that's not a numerical value. We say the limit does not exist when it's not a numerical value.

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