Learn how to solve limits by rationalizing problems step by step online. Find the limit of 4x(x^(1/2)-(x-1)^(1/2)) as x approaches infinity. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. Multiply the single term x by each term of the polynomial \left(\sqrt{x}-\sqrt{x-1}\right). When multiplying exponents with same base you can add the exponents: \sqrt{x}x. Applying rationalisation.

Find the limit of 4x(x^(1/2)-(x-1)^(1/2)) as x approaches infinity