Bra-kets and operator formalism in QM - Expectation values of momentum

[Dixanadu]

Homework Statement

sup guys!

I think I've solved this set of problems, but I was just wondering if I've done it right - I have no way to tell. I'll put all the questions and answers here - plus the stuff I used. So could you please tell me if there's any mistakes?
Here it is - using Word as always!
http://imageshack.com/a/img4/750/6i29.png

Homework Equations

http://imageshack.com/a/img266/4082/58m3.jpg

BTW - I just realized I put in the transpose symbol instead of the dagger - i meant the dagger for the raising operator!

The Attempt at a Solution

http://imageshack.com/a/img546/7347/1oty.jpg

 

[1ndranil]

My solutions are here, have a look..

 

[Judas503]

If you are careful with the manipulations of the operators, it's an easy problem.