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Problem 4 Medium Difficulty

Use the given graph of $ f $ to state the value of each quantity, if it exists. If it does not exist, explain why.

(a) $ \displaystyle \lim_{x\to 2^-}f(x) $
(b) $ \displaystyle \lim_{x\to 2^+}f(x) $
(c) $ \displaystyle \lim_{x\to 2}f(x) $
(d) $ f(2) $
(e) $ \displaystyle \lim_{x\to 4}f(x) $
(f) $ f(4) $

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Video Transcript

in this problem, it is us that use the given graph of F to state the value of each quantity if it exists, If it does not exist, explain why. Right? So here it is given the first one limit exchange. Two to minus of fx you can say. So here the value is nearer to value of Y is nearer to, you can say here, you can see or if it will be closer to three. So the value becomes three here. Okay, so this is the answer secondly, for part B we will see limit extends to two plus efforts is given to us. That means For ex all equals greater than two only. This limit exists. Right? So that's why values three years, which is closer to, you can say do cool, X is equal to two. Now limit extends to two of fx. Fx is nothing but the value of Y at x is equal to two years assuming rate. So now this value is not defined because there are two reasons because there is an open daughters present right now. And secondly we can say limit, Extreme 2- is not equal to limit Extends to two plus for the function of X. That is why you can say now at F equals to two which is a defined value. The defined value is nothing but this is three. So this is our answer now for the party limit ethics Limit exchange to four of FX that is undefined. You can see this value is and define hi, good thing because again, there is open and open dot here. Right? So that's why this becomes a no defined values are present at X is equal as his exes equals to four years. Now. Again, f ford it is asked. Okay, so is there any value which is which is there in the defined value for airport? No, because again there is an open he looks open loop, you can say open point, you can say all, you can say the open dot, Right? So this is does not exist undeclared. Hello everyone. Yeah, So this is all you can say undefined can be written as does not exist, does not exist. So this is how we solve this problem. I hope you understood the concept. Thank you for watching.