#1.

Do L'hopital twice.

That is, take the derivative of the numerator and denominators twice

The second derivative of is 2.

You have:

Now, as x approaches 0, you have1/2

For #2. I believe you may have a 'tan' in your future.

For #3.

Equate coefficients:

Solve the system.

Soroban has a slick way of doing partial fractions. I trust he'll be along to demonstrate.