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Evaluate each limit (if it exists). Use $L$ Hospital's rule (if appropriate).$$\lim _{\theta \rightarrow 0} \frac{\tan \theta}{\theta}$$

1

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 7

L'Hospital's Rule

Derivatives

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Mhm. So we're asked to evaluate the limit as data approaches. zero of tangent of data divided by data. Now you might need to if you're doing direct substitution, think about the unit circle. And how if data is equal to zero, we have the order pair 10. And tangent by definition is Y over X. So as you're looking at that, well zero divided, I want to be zero. So tangent of zero is zero. And same thing with the denominator. If I'm just doing direct substitution uh and replacing data with zero, Then what we have is the form 0/0 is the indeterminant form. Uh And determinant which is telling us to use the local tiles route. I was always taught to use a lot of errors when doing the lumpy tiles rule. That's why I do this over and over again. Okay. So how do we do locate eligible? First of all, the limit as data approaches, zero is the same. And you just take the drift of at the top of the drift of of the top the derivative of tangent is seeking squared. And then you do the drift of the bottom drift of what data is one. Well, now, when I do direct substitution we have second of zero being squared. And just a reminder seeking is one over co sign. And if we're looking up here as I drew, it already is co signs. The X coordinates. We're looking at 1/1 squared. Uh and one square is just one. So the correct answer back to the original problem is the eliminates data purchase zero tangent. Theta or theta is one. Mhm.

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