Indeterminate limit of the form 1/0

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SUMMARY

The limit lim(x->1) (1+2ln(x))^(1/(x-1)) is evaluated as an indeterminate form of 1^(infinity). By letting y = (1+2ln(x))^(1/(x-1)) and taking the natural logarithm, ln(y) results in an expression that approaches 1/0, indicating that the limit does not exist. However, a calculation using MS Mathematics yielded a limit of e^2, suggesting an arithmetic error in the manual evaluation. The discrepancy highlights the importance of verifying calculations with reliable software tools.

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When finding lim(x->1) (1+2ln(x))^(1/(x-1)) = 1^(infinity) I let
y = (1+2ln(x))^(1/(x-1)) then ln both sides giving
ln(y) = ln(1+2ln(x)))/(x-1)
Taking the limit of ln(y) gives 1/0, which is indeterminate and hence the limit does not exist.
However, I typed this into MS Mathematics and got the limit as e^2.
Help please.
 
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I made an arithmetic error. Nevermind.
 

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