Question

How do you evaluate limit of `(x^a-1)/(x^b-1)` as x approaches 1?

Answer 1

Factor and reduce.

Explanation:

`lim_(xrarr1)(x^a-1)/(x^b-1) = lim_(xrarr1)((x-1)(x^(a-1)+x^(a-2)+ * * * x+1))/((x-1)(x^(b-1)+x^(b-2)+ * * * x+1))`

`= lim_(xrarr1)(x^(a-1)+x^(a-2)+ * * * x+1)/(x^(b-1)+x^(b-2)+ * * * x+1)`

`= a/b`