Question

`lim_(x->3) (x^5 - 243)/(x^3 - 27)` = ?

Options

• `17/3`

• `5/2`

• 15

• 1

Answer 1

15

Explanation:

`lim_(x->3) (x^5 - 243)/(x^3 - 27) = lim_(x->3) (x^5 - 3^5)/(x^3 - 3^3)`

`= 5/3 (3)^(5 - 3)`

= 15   ....`[because lim_(x->"a") (x^m - "a"^"m")/(x^"n" - "a"^"n") = "m"/"n""a"^("m - n")]`