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(a) What is wrong with the following equation?$$\frac{x^{2}+x-6}{x-2}=x+3$$(b) In view of part (a), explain why the equation$$\lim _{x \rightarrow 2} \frac{x^{2}+x-6}{x-2}=\lim _{x \rightarrow 2}(x+3)$$is correct.

A) $\frac{x^{2}+x-6}{x-2}=x+3, \quad x \neq 2$B) $\lim _{x \rightarrow 2} \frac{x^{2}+x-6}{x-2}=\lim _{x \rightarrow 2}(x+3)$

Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 4

Calculating Limits

Functions

Limits

Continuous Functions

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Lectures

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In mathematics, the limit …

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(a) Find the error in the …

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Which one is correct, and …

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$$\lim _{x \rightarrow-3^{…

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a. $\lim _{x \rightarrow 2…

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Explain what is wrong with…

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Find the error(s) in the i…

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Find the limits.\begin…

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$$\lim _{x \rightarrow(-1 …

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$\lim _{x \rightarrow \inf…

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Find the limit if it exist…

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a. Evaluate $\lim _{x \rig…

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$$\text { a. } \lim _{x \r…

01:05

So when we have this one, uh, um X squared the X minus six over, uh, X minus two eight holes. Uh, expose three. The reason why this thing here is not correct. Start correct to say is because there's should be a condition for the denominator, right? This should be a condition, because X cannot take any value at all. You can take some values, but not just any value. That should be some restrictions. So usually when you do those, you know, when X is to, this becomes zero. And this, uh, rational functions become non existence, right? So usually should put a condition that X is not equal to positive, too, actually, because positivity is gonna be here. Zero. Right. So if you write those one without this condition, then this is not correct, right? It is a condition that makes it correct. So it means that whatever value that s can take, X cannot be positive to write. That is how you can correct it. Eso that is wrong with that equation. Uh, no. Uh, let's to get this one there. It as X approaches to of the function, right. So rational function here limits except history of experts. Three. Right. So what is this one? Uh, no, The reason why this one is correct here is because no for limits you before so doing work, right? Because when you put in to here, this is gonna be to square, which is four plus two, which is six. So the numerator is gonna be zero. The denominator is gonna be zero when you have 00 And this means that you have to do or work right Have work to do because you have zero syrup, right? Somebody can use local tiles rule. You can do many, many things. There are many ways you can go about it. But if you have 00 is an indeterminate for right, indeterminate, indeterminate, for so easily used local tiles rule. Or you can do many other things, right? There are a lot of things you can do in situations like this. When you have something like zero off the zero, it is part of the indeterminate form, so you just have to do all the work. So we're gonna factored in numerator. That is also another way to go about it on your factor of the numerator. You can see that this is gonna be X minus. Do experts three. And that is the kind of way it will be right in this one. And they have experience too. So you can see that here. The next one is to cancels this one. Right? So the left hand side of the entire thing becomes limit. X approaches two off that and the right hand side. Is this one, right? Any exactly equal. Right, So this is correct.

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