How to solve limit of the function? Limit[(1 + (Tan[Sqrt[x]])^2)^(3/x), x -> 0] I'm getting answer from Math program = e^3 How do we get there?
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Originally Posted by RCola How to solve limit of the function? Limit[(1 + (Tan[Sqrt[x]])^2)^(3/x), x -> 0] I'm getting answer from Math program = e^3 How do we get there? Suppose the limit exists and is equal to then take the natural log of both sides to get Now we can apply L'hosiptials rule Now the limit is
Originally Posted by TheEmptySet I don't understand why this expression is here. (ln|x|)' = 1/x Maybe it's composite function. So how do we get this line?
Originally Posted by RCola I don't understand why this expression is here. (ln|x|)' = 1/x Maybe it's composite function. So how do we get this line? By the chain rule Now by the chain rule again This is 3 function compositions. Now just sub in to get
Is it easier if you write the function as ?
Originally Posted by Prove It Is it easier if you write the function as ? Is equals to ?
It most certainly is. . In this case .
Thanks a lot for your help guys!
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