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# Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.$\displaystyle \lim_{x\to 0} (\csc x - \cot x)$

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Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

Okay. The first thing we can do is we can rewrite this so it's easier to manipulate. Won over. Sign of acts minus co signed X. We're sign Axe. When we plug in, we simply end up with zero all over again. Therefore, we know we have to use the hoppy tolls. Rule the derivative of one issue zero the derivative of negative coast on Axis. Positive sign ups. The derivative of Sine X is co sign axe. Pretty straightforward the end of the zero for one, but this gives us a solution of zero.

#### Topics

Derivatives

Differentiation

Volume

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp