## Limit of (x^n-a^n)/(x-a) as x approaches a: Formula, Proof

The limit of (x^n-a^n)/(x-a) as x approaches a is equal to nan-1. This limit is denoted by limx→a (xn-an)/(x-a), so the limit formula of (xn-an)/(x-a) when x tends to a is given as follows. limx→a (xn-an)/(x-a) = n⋅an-1 Lets prove this limit formula. Proof of limx→a (xn-an)/(x-a) To prove limx→a (xn-an)/(x-a) = n⋅an-1 we will consider three different cases … Read more