Prove that when c ∈ N:

a)

lim [(1+x)^(1/c) - 1]/x = 1/c

x->0

b)

lim [(1+x)^r - 1]/x = r

x->0

,where r = c/n

My approach for a and b are pretty similar, i get stuck at the same point.

For a, i multiplied the numerator and the denominator by [(1+x)^(1/c) + 1] to get rid of the radical on top. This left me with:

Lim 1/[(1+x)^(1/c)+1]

x->0

This is where im stuck, if i find the limit of the numerator and divide it by the limit of the denominator, i dont get 1/c. So im clearly doing something wrong.

As for part c, i pretty much use the same approach and get:

Lim 1/[(1+x)^(r)+1]

x->0

which also doesnt lead to the answer.

Please help.