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If a limit tends to infinity, it exists or not? What is the value of lim x tends to zero (1/|x|)?

If a limit tends to infinity, it exists or not? What is the value of lim x tends to zero (1/|x|)?

Grade:12

2 Answers

Arun
25758 Points
3 years ago
Dear student
 
lim x tends to 0 1/|x| = imfinity,
 
but in technical terms , wesay that limit doesnot exist
Aditya Gupta
2081 Points
3 years ago
this is an extremely good ques and even i had a doubt when i first came across this dilemma. 
basically, a limit is DEFINED to exist IFF it is finite and unique. hence, whenever a limit is infinity, it is said that the limit does not exist. to be more specific on lim x tends to zero (1/|x|), we say that the limit is infinity and hence does not exist (note how we say that “the limit is infinity” and not “the value of the limit is infinity”).

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