Learn how to solve problems step by step online. Find the limit of (2x-2x^2)/(x-(2x-x^2)^(1/2)) as x approaches 1. The power of a product is equal to the product of it's factors raised to the same power. Factor the polynomial 2x-2x^2 by it's greatest common factor (GCF): 2x. 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)}. If we directly evaluate the limit 2\lim_{x\to1}\left(\frac{x\left(1-x\right)}{x-\sqrt{x}\sqrt{2-x}}\right) as x tends to 1, we can see that it gives us an indeterminate form.

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