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Evaluate the limit, if it exists.$\lim _{t \rightarrow 0}\left(\frac{1}{t}-\frac{1}{t^{2}+t}\right)$

1

Calculus 1 / AB

Chapter 2

Limits

Section 4

Limits: Algebraic Methods

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Hey, everybody, we're doing Chapter two, Section four Problem 22. So whenever whenever I get problem like this, I have to think about what is my my plan of action, right? Some problems. It's like trying to trying to simplify a problem into one fraction. Sometimes it's trying to make it so that things ahh factor and all that happens. So this I'm gonna tell you my my thought process, and hopefully you'll find that helpful. So the main issue with this problem that you start out as if you plug in zero and you get one divided by zero minus one, divided by zero. Okay, well, that's not helpful. So there are two ways for me to think about doing this. One is I wanna simplify the fractions for a second. I have won over T minus one over tee times T plus one. Okay, Now I go into one of two paths. I see that the right fraction has a tea and a T plus one of the bottom and the left one on Lee Hesitate so I could multiply the left one by t plus one over T plus one. Get a common denominator combined them hope that a T cancels and then you go. That's one way of doing it, Thea. Other way of thinking about it, at least in my mind. Waas you could you could try to see the limited them both individually. The problem is that then you just have to individual ones that don't work. So that's not super helpful. So I want to handle the first plan. So that means that I need to multiple like this 1st 1 by t plus one over t plus one. And so when I factor it, I get t plus one minus one because I combine the fractions over tee times T plus one. I see that the one and the negative one cancel and then I have a tea and the tea canceled by dividing. So then you're just left with one over T plus one. Now that looks pretty good to me, because if I plug in zero for T, I just get one over one, which is one, and that is a limit that exists. And that means that that was a good way of doing it. So hopefully you seeing me run through the thought process is helpful and and then getting, you know, all the way from the limit and then going down into the factor and then doing the math on it and then getting your final answer was helpful for you. Okay? Until next time.

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