Math Help Forum: Verify the limit

Hi i didn't understand how i verify this limit:



thank you

Since the function is continuous, just substitute x = 8...

That is, if the conditions of the problem allow you to assert that this is a continuous function! You might not have studied "continuos" functions yet or the point of this might be to show that x^(1/3) and x^{1/3}- 2 are continuous at x= 8.0

If so, you will have to go back to the definition. Given epsilon> 0, how close to 8 must x be to guarentee that x^(1/3)- 2= 0?
It might note help to note that (x^(1/3)- 2)(x^(2/3)+ 2x^(1/3)+ 4)= x- 8.