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A question from limits . could you please tell how to solve this problem

A question from limits . could you please tell how to solve this problem

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Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
So I assume we have to find the limit of f(x) as.x tends to 0.
Right hand limit RHL= Lt x tends to 0+ x/(1+e^(1/x))
= 0/(1+ infinity)= 0/infinity= 0
Similarly LHL= Lt x tends to 0- x/(1+e^(1/x))
= 0/(1+0)= 0
Note that we have used results like e^(-infinity)= 0 and e^infinity= infinity and 1/x= infinity when x tends to 0+ while 1/x= - infinity when x tends to 0-.
Hence the limit at 0 exists and is equal to 0
Or Lt x tends to 0 f(x)= 0
KINDLY APPROVE :))

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