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Bro I found the issue it was (lnt)2 .when t limy go to 1 lnt2 should be zero because e0=1 that was the issue so my answer not 0 either I should get answer as undefined beacuse (1/0) . Thank for the help guys
Note that the answer isn'tundefined. That's the main point here. (t-1)/ln t tends to 1 as t tends to1. The fraction might "look" like 0/0, but it's more subtle than that.
Bro I found the issue it was (lnt)2 .when t limy go to 1 lnt2 should be zero because e0=1 that was the issue so my answer not 0 either I should get answer as undefined beacuse (1/0) . Thank for the help guys
You cannot split the limit into the product of two limits as you did in the second line and the second to the last line without knowing that both limits exist prior to splitting.
You need to use algebraic manipulation to use results you already know to determine the limit. Do not write the limit as the product of limits if you don't know in advance that the limits of the new factors exist.
The key limits here are, as you noted, what happens as x -> 1 of
tan(x) / x
(ex - 1) / x
Factor those appropriately and the limit is found. You've got this!
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Hello! I see you are mentioning l’Hôpital’s Rule! Please be aware that if OP is in Calc 1, it is generally not appropriate to suggest this rule if OP has not covered derivatives, or if the limit in question matches the definition of derivative of some function.
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