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If $$\lim _{x \rightarrow 1} \frac{f(x)-8}{x-1}=10,$$ find $$\lim _{x \rightarrow 1} f(x)$$

8

Calculus 1 / AB

Chapter 1

FUNCTIONS AND LIMITS

Section 4

Calculating Limits

Functions

Limits

Continuous Functions

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you have limits the limits. X approaches one of ffx minus eight Over, uh, experience one. We have this asked. 10 given, Right. Eso When is the limit? As X approaches one off ffx. Right. So what is the limit as executions one of FX. Okay, so? So we want to find this one. Ah, you know, this limit exists Limit except delicious one. Ah, for F of X minus eight. This one exists. And how do we weaken this dysfunction? Here is the same ass, right? In F off X minus eight over X minus one times X menstrual. This is the same as this, right? Because this is gonna cancel this one. Ultimately. And they gonna have this guy again, right? So nervous, saying I'm just rewritten in a differently street. Egypt. So you wait. Right? So this is the same thing now. We knew that we can separate those limits. This limited the same as limit. Except for which is one every thanks. Minus age over minus 8/1 and times limit. Except for X. A precious one of those who can split the limits. Right? We know that We know what this limit is. It has been given, right? That limit ISS 10. Right here. So? So here is gonna be 10. Mortified by the limit as X approaches one except wishes one except religious one of this. When you put one here, this is gonna be zero. Right? So this is you know, so, actually, the limits as X approaches one off F X minus eight has been shown to be zero. Right now we want a fine the limit of just FX. So how do we write it? No. In the middle of every face, everything X minus eight Ever fix can also be written as f off eggs minus eight plus eight. You can write it like that. Just sort of Samos after face. We're using it because we have our results. Now we can use immediately. Right? So this one is also the same as the limit except which is one off every face minus eight, then plus the limit exit, which is one of eight. Right. The limit laws houses to do this. Now, what is this one where we found that that one is here, here. Simply said that within a zero. So this is gonna be zero and then. Plus, what is the limit? This limit? Well, this Let me Here is eight, right? Therefore, this limit the limit of this one is eight.

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