please solve it let f be the function defined over { 0 , ∞ ) as ∫ f(x) = x(ln(x)-1)^2 for x>0 and let (c) be its representative curve , we admit that f is continous at x=0
a ) determine lim f(x) / x as x approaching 0
b) find lim f(x) as x approaching infinity and lim f(x) /x as x approaching infinity
c ) for x > 0, verify that derivative d/dx f(x) = (ln(x))^2 - 1 and set up the table of variation of f