I'll attempt problem 1.
(1) I divide the numerator and denominator by n which yields
(2) There's a formula if a>0, then
(3) Since from (1), I use u-substitution. I let u =
(4) By u substitution the integral becomes
. Edit:No, this is not correct. Scratch this.
(5) Applying the formula (2) with (4) with get
(6) As for the limit,
For problem 3, I believe there's a typo.
should it be
I'm sure I have to use the Squeezing Principle for this. I can't seem to integrate sin(x)/x in terms of elementary functions. I'm guessing I can integrate this using the Taylor series for the sine function, but I have no idea after that.