Learn how to solve problems step by step online. Find the limit of (3x-2)^(1/2)-x as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Rewrite the fraction, in such a way that both numerator and denominator are inside the exponent or radical.

Find the limit of (3x-2)^(1/2)-x as x approaches infinity