I got a question on my test today and I spent a great deal of time on the question.

lim as x -> 27 (27-x)/[(x^1/3)-3]

I was able to approximate the limit by evaluating left and right of 27; however, there was another method where a change of variable was used, for example let u=(x^1/3).

I was unsure how to proceed this way. any help would be appreciated.