f(x) = {3-x, x<2 2, x=2 x/2, x>2 } Find value of lim x--> 1- and lim x--> 1+. Does lim x--> 1, exist or not? Explain why?
Answer (1)
29th Oct, 2020
Hello Dear,
Well, to check for limit, its left hand limit, right hand limit and actual limit must all be equal, So,
for x=1, f(x)=3-x; since f(x)=3-x for x<2 (and obviously 1<2)
So, for Right Hand Limit f(1+h)=2-h=2 (putting h=0, where h is very small and positive)
Similarly for Left hand Limit f(1-h)=2+h = 2 (and putting h=0, where h is very small and positive)
And at x=1, f(1)=2;
Hence, all three limits exist and are equal, so lim x--> 1 for f(x) exists.
(My opinion, its limit is changing at x=2, either you have miswritten this question, or this question is way easier and trying to say that limit doesn't get affected if function doesn't change)
Hope this helps, and feel free to ask any further query...
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Comments (2)
29th Oct, 2020
After many weeks got a reply, but still cleared my doubt...Thank You
Reply
30th Oct, 2020
Ayush Singh
Hey! Ayush, I am surprised too! why anyone didn't answered your query, and I've found your query in unanswered first section of mine, I hope next time you get a quick reply, ByTheWay, happy to see your doubt cleared, ask further questions of mathematics, if you find difficult, we are always there to help you! Good Luck!
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