To compute this limit. We're gonna use the expansion of the cosine in Taylors series. We after that, we're going to use the natural log as an expansion on tailored series around zero. And after that, we can collect like terms that go to zero. And we take the limit as X goes to zero. And from that, we can see that our limit here is 1. So this Berkeley math. Tournament question is important. It's using a lot of calculus idea, like derivatives expansions on series and limits and derivatives to arrive to the formula. So Berkeley math. Tournament question here is very important, so we solved this problem. So here we have all the solutions that we need for this kind of questions. So this is one way of solving. This problem. We can get more ways, like, using low titles, or to solve this question. But remember that, when we expand in series, we are working around some point closer. Zero we can work on something close to Infinity if we want. But remember here. We are interested in the limit as X goes to zero. So therefore we are working or using tailors series close to zero. Okay, so these this Berkeley math. Question is very important, a Harvard MIT Stanford Princeton, all of them, use this kind of problems. So if when I learn more and get an idea, this is the good start. So use limits derivatives integrals and different kind of switching the limit and integrals, use a series of functions and sequences of functions to get the limit that you need. We are here to help you. So this video can be helpful to students to teachers trying to get the Olympia or working AP calculus or trying to get their monthly sensor exam like the practice 5161 test. So here we are help. Where willing to help all the students in solving this kind of questions, this is great question and it's good to learn more techniques and more ways of solving algebra and calculus problems.
