Question

How do you find the limit of `(3x-3) /( x^4 - 12x^3 + 36x^2)` as x approaches `3^+`?

Answer 1

`= 2/ 27`

Explanation:

`lim_{x to 3^+} (3x-3) /( x^4 - 12x^3 + 36x^2)`

`= lim_{x to 3^+} 1/x^2 * lim_{x to 3^+} (3(x-1)) /( x^2 - 12x + 36)`

`= 1/9 * lim_{x to 3^+} (3(x-1)) /( x-6)^2`

`= 1/9 * (3(3-1)) /( 3-6)^2`

`= 2/ 27`