Limit of |x|/x as x approaches 0 Does Not Exist | Calculus 1

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We show the limit of absolute value of x over x, as x goes to zero, does not exist. This is because as x approaches 0 from the left, it is negative, so |x| = -x, and then |x|/x = -x/x = -1. However, as x approaches 0 from the right, it is positive, so |x|/x = x/x = 1. Thus, the one sided limits are different and so the two sided limit does not exist. #Calculus1

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Комментарии
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Currently studying for JEE exam and got stuck on 1st question of limits 😅. Thanks for explaining though

tadipaar
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This question appeared in a list of exercises for Calculus 1 and I didn't understand why the answer was 1 and -1 and just seeing the first explanation of 0-, I understood why. Thank you very much!!!!

rosanepaula
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You are an excellent teacher Mr. Wrathy! 👏

arjunob
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could you do a proof for this same problem?

daliobenavidez
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Hello, can I please ask you a question on subsets? how many subsets of {1, 2, 3, …, 20} are there with no more than 2 consecutive integers? Can you please explain step by step how to arrive at the answer?

zacksnyder
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I am new to this subject please help me : when x reaches from the left side (negative) the absolute value of it or mod will positive x then why is it -x

codewithdevhindi
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More context: This is the derivative of the absolute value function which has a sharp corner at the origin.

Abs(x)=sqrt(x^2), chain rule leads to your result.

You must of had your coffee before the video today 😊

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