find the derevative (hint try to use limits)

Question

(x^2010 - 1 )\(x -1 )as x approaches1

Answer 1

by definition...

f'(x)= lim (f(x+h)-f(x)/h)

= lim ((x+h)^2010-1/(x+h-1) - (x^2010-1)/(x-1)

Now, expand the first numerator with the binomial expansion, but stop on the second term, because you know h is going to zero.

combine fractions,take h tozero, then x=1, and you get the limit.

Answer 2

what he said