Proof for this hard limit without differentiation,l'Hospital or Taylor series

[wolly]

I have another limit where I'm struggling with the solving.Can somone help me?

I used a method like this but I'm not 100% if it's correct!

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What should I do from that step? I know something like arctan(x)/x when x tends to 0 is 1. How is that going to help me?

 

[tkhunny]

I have a burning desire to simplify this: [math]atan(tan(atan(1+x)-atan(1+x)))[/math]. Start from the inside.

I wonder where that could lead...

Try that numerator again. There are rules for logarithms. That wasn't it.