We have f(x) = x^300 + x + 1 and we have to find

lim x-->1 [ (f(x)-f(1))/(x-1)]

=> lim x-->1 [ x^300 + x + 1 - 3)/ (x-1)]

for x = 1 we have the form 0/0, so we can use l'hopital's rule

=> lim x-->1 [ 300*x^299 + 1 )]

for x = 1, we have 300*1 + 1 = 301

**The required limit of the function is 301**