What kind of help do you want? What definition of "continuous" are you using? Do you know that "f(x) is continuous at x= a if and only if, given a sequence that converges to a, converges to f(a)"? If so then consider a sequence made entirely of rational numbers and a sequence made entirely of irrational numbers, both converging to a.

As far as "differentiable" is concerned, the derivative at x= 0 is defined as . Again, you can look at all sequences that converge to 0.

For (5) an obvious "appropriate function" is x- 1- ln x. What is the derivative of the that? What does that tell you?

Since (6) says "By considering primitives for ", whatisa "primitive" (integral) for that function. You might also want to note that and think about the sum of a geometric series. That will allow you to write as a power series. What is the term-by-term integral of that?