Unsuccessful Attempts at Solving Limit Questions

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The discussion centers on the evaluation of limits for two functions: (1/(x-1)) as x approaches 1 from the left and (3+(7/x)) as x approaches 0 from the right. The first limit does not exist because the left-hand limit approaches negative infinity while the right-hand limit does not converge to a finite number. Similarly, the second limit also does not exist in a conventional sense, as it approaches positive infinity from the right side, indicating that the limit is undefined without specification of the direction of approach.

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anil
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Hello I have been making unsucessful attempts in answering these following q's.

Find Limit of (1/(x-1)), as X approaches 1-. I got the answer as "Limit doesnot exist" but not sure.

Find Limit of (3+(7/x)), as X approaches 0+. I got the answer as "Limit doesnot exist" but not sure.

Any one know the answer?
 
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Your answers are correct as long as you (or your teacher) define limits as finite numbers. Otherwise the first problem has -infinity while the second has +infinity.
 
The limit for the first function indeed does NOT exist. Infinity is different than not existing, because for a limit to exist at a certain X Value, the limit that you obtain when approaching from the left side must be the same as the limit that you obtain from approaching from the right side, and in those functions, they do not, therefore the limit is not infinity, but is non-existant. The limit for the second one cannot be said as existing just because it is not specified if it is the limit from the negative or positive side, and the limit only exists when coming from the negative side.
 
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