Answer: To find the limit of the expression 3√x-1/x-1 as x approaches 1, we can use L'Hopital's Rule. L'Hopital's Rule is a method for finding the limit of indeterminate forms, such as 0/0 or ∞/∞, by taking the derivative of the numerator and denominator.
In this case, the expression is of the form 0/0, so we can use L'Hopital's Rule:
lim 3√x-1/x-1 = lim (3/2)((x-1)^(1/2)) / 1 = 3/2
So the limit of the expression 3√x-1/x-1 as x approaches 1 is equal to 3/2.
Explanation: