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