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Find the limits. $$\lim _{x \rightarrow 0} 6 x^{2}(\cot x)(\csc 2 x)$$

Calculus 1 / AB

Chapter 2

Limits and Continuity

Section 4

One-Sided Limits

Limits

Continuous Functions

Oregon State University

Harvey Mudd College

Baylor University

Lectures

03:09

In mathematics, precalculu…

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$$\lim _{x \rightarrow 0} …

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Find the limits.$$…

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Find the limits$$\lim …

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Determine each limit.$…

All right, so in this video were asked to find them. Limit is exposed to 06 x squared times co tangent, X times, Corsican two x And we're supposed to use the fact that the limit SK goes is euros. I, Katie, but by Kinko's first thing we're gonna do is we're gonna try to manipulate what we have inside the limit. So reversible since we're looking for something like sine sine X divided by X. So we're going to try to convert court engine into terms of sided co sign. So we know that the co tangent is just courtside X divided by acts. So we have this right here, and we also know that CO seek out to Rex is just one divided by side. And then now we're gonna try to split our six x squared in such a way that whatever we have inside the sign is going to be found in the numerator. So, for example, here we have sine X, So we're gonna pull in X from that 66 square Here we are here. We have to act. So we're gonna pull it two x from the six x square. So now we're left with three times. Co sign X multiplied by X divided by sine X multiplied by two x divided by sine two wings. So we're gonna take our manipulation. But we did right here. I'm gonna plug it in to we're gonna substitute it in toward limit as experts to zero. So now we have three times co sign next multiplied by another way to write X divided by sine X We can write it as the reciprocal of sine X, divided by x So here we have one divided by sine X divided by X And again we can also do that same trick in right It's two x divided by sine toe Xs one provided by signed two extra biotic Plato And now we take the limit as excuse to zero. So the three years of constant so stays the same Now coastline X as X goes to zero. This becomes one because if we plug in zero, we get one fear That denominator becomes one. But we have one divided by one So that also this one again Here we have Wonderful. It will be one divided by one which is again one. So we have three times, one times one times one. So our final and source of the limiters exposed to zero this three.

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