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Find the limitsHy[([email protected] +2)+cs+74444] He;-xi+st-] #[22.+*+#5-2"]...

Question

Find the limitsHy[([email protected] +2)+cs+74444] He;-xi+st-] #[22.+*+#5-2"]

Find the limits Hy[([email protected] +2)+cs+74444] He;-xi+st-] #[22.+*+#5-2"]



Answers

Find the limits $$\lim _{x \rightarrow 0^{+}} x^{2} \ln x$$

So if this problem were asked to evaluate the following limit. So it's important that when we evaluate a limit, we understand what we're looking for. So if we have to say for example, the sign of acts, we know that when we're evaluating say the limit as X approaches pi over two, um that we want to look what the value that we're approaching as we approach from the left. And what is the value that we're approaching as we approach from the right, it doesn't actually matter what's happening at the actual function itself. Like for example, if we had the sin of X over X, we're approaching zero. We see the function is not defined at zero, but the limit does exist because as we approach from the left, it's clear that we're approaching one and as we approach as we approach from the right, it's clear we're approaching one and as we approach from the left it's clear we're approaching one as well. So with that information available were able to identify the limit in this case for the problem were given. We see we can do the same thing. And when we evaluate the limit, we end up getting pie as our final answer

This man is.

Send the current problem. We have to evaluate the given expression. Okay. Andi? Yeah. So what is our first approach? All the times we always know that any given problem, we start with method off direct substitution. And when it does not work out, we try to go for other path, right? Any other way? Be the two part test or be the polar transformation. Right. I keep on repeating at the beginning off every video, expecting that Whichever video you pick to listen, you know what is a standard? We just try when you try to solve any problems on limits. So the idea here is X reaches 21 Why reaches toe Ellen too, and said reaches 23 So in this expression, wherever we get these observations in the place of said, we will plug three in the place off. Why? We will plug in log toe and in the place off X, we will substitute one on and in the next step. That's why when we write easy equals two, we will actually have these values substituted so no longer we will write this huge expression. Okay. Why? Because we will understand that X has already attained the value one so we don't have toe. Uh, make sure we don't have to write the expression in the beginning of the statement. All right. So I will clean up the screen. Where you better understanding. And then here I go. So what does it do? Zed is three. Correct. So hence I write three into e to the part, right? It the part x X goes to one. So I substitute one into Where does Waigo Why goes to Ellen too? So, Ellen to No, If you remember, eat to the power log. Mhm X is nothing but X. That means any number. If I have five over here, I can write five over here. U to the power log. Basie and Ellen is nothing but log with this e correct. So that's why we will go ahead and we can right over there that this entire expression will become. Eat the power off course. One into Ellen to is nothing but Ellen too. So we can write, See into to. So this expression is nothing but one into Ellen. To means Ellen to so e to the power Ellen do is nothing but to this is a very elementary expression. Let me know in the comment box if you couldn't understand Andi. That's how we come to the answer on board. In case you have any questions, let me know in the comments section. Have a good day. Bye bye.

Okay, so we call that sequence weaken very that as co sign, that's one over co sign of X and now using our kosher girl, we can rewrite this as the falling over delimit as X approaches zero of coastline of X. What that's equal to one over co sign at zero, which is equal to 1/1, and that's equal to one.


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