1. Find (f^-1)'(0) if:

integral sign x, 0 1+sin(sint)dt.

2. Find a function g such that:

integral sign x, 0 tg(t)dt= x+x^2

3. Find all continous functions f satisfying:

integral sign x,0 f=(f(x))^2+C. for some constant C.

4. Find F'(x) if F(x)= integral x,0 xf(t)dt. (The answer is not xf(x); perform obvious manipulatipon on the integral before trying to find F'.)

5. The limit lim integral sign N, a f, if it exists, is denoted by integral sign

N-> alpha

integral sign (alpha, a) f

a) Determine integral sign alpha, 1 x^r dx, if r<-1