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Problem 38 Medium Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to \pi^-}\cot x $

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Adam R.

March 13, 2019

Video Transcript

evaluate this limit. Note that the cogent identity for coat engine tax is co sign X over Synnex. And so we can rewrite this as the limits as X approaches pie from the left of co sign X over Synnex, which is equal to the limit. As X approaches pie from the left of co sign X times the limited as X approaches spy from the Left of one over Synnex. Now, if we evaluated pie, we have co sign of pie times. You have limits as X approaches by from the left of one over Synnex know that if we substitute pie for X in side effects that become zero. So The value of one over sine x becomes undefined. That means we need to look closely on the value of one oversight next as we move closer to bye from the left. Now if we approach pie from the left side, that means the angle is in the second quadrant where sign is positive, so the value of sign here is a small positive number, which means that the value of one over sine X is a positive infinity. And so and here we have Co signed pie which is negative one times positive infinity. This gives us a limit which is equal to negative infinity.