00:01
So in this first question you were asked for the limit, has x approaches pi over 4 of the tangent of 2x? now, if you tried to plug in, you would get the tangent of 2 times pi over 4.
00:18
You would get the tangent of pi over 2, which is undefined.
00:29
And i claim this limit is not going to exist.
00:33
Here's why.
00:36
If you look at the graph of y equals the tangent of 2x, this graph is going to have a vertical asymptote at x equals pi over 4.
00:54
And there's also a vertical asymptote at x equals 0, by the way, and another vertical asymptote at x equals pi over 2.
01:03
There are vertical asymptotes every pi over 4 units on this graph.
01:10
And between these vertical asymptotes, you have these things that sort of look like squished cubics.
01:21
So my relevant vertical asymptote here is x equals pi over four, which is in here.
01:30
Specifically, if i looked at the limit as x approached pi over four from the left of the tangent of 2x, when i'm a little bit to the left of pi over four, the y values on this.
01:44
Function, they approach positive infinity.
01:50
But if you look at the limit as x approaches pi over 4 from the right of the tangent of 2x, as you get closer and closer to x equals pi over 4 from the right, the y's just keep going down, the y's are approaching negative infinity.
02:09
Since the limit from the left and right, since those limits are different, we would say that the limit as x approaches pi over four overall for this function does not exist.
02:28
Okay...