Curious how many of these can be tackled directly by a modern symbolic math package like Mathematica. Question 2 in particular, I'd be curious if it can get th

Curious how many of these can be tackled directly by a modern symbolic math package like Mathematica. Question 2 in particular, I'd be curious if it can get there without guidance. [EDIT]: Answer is yes: https://www.wolframalpha.com/input/?i=Limit%5B%28Sin%5BTan%5Bx%5D%5D+-+Tan%5BSin%5Bx%5D%5D%29%2F%28ArcSin%5BArcTan%5Bx%5D%5D+-+ArcTan%5BArcSin%5Bx%5D%5D%29%2C+x+-%3E+0%5D https://www.wolframalpha.com/input/?i=Limit%5B%28Sin%5BTan%5...