Question

Find the limit for lim x--->4

(4x-x^2) / (2-sqrt x)

Answer 1

Take the conjugate of the function. Can you do that?

Answer 2

multiply by conjugate*

Answer 3

It's 2+sqrt x right?

Answer 4

Yes.

Answer 5

\(\bf \cfrac{4x-x^2}{2-\sqrt{x}} \times \cfrac{2+\sqrt{x}}{2+\sqrt{x}} \implies
\cfrac{x(4-x)(2+\sqrt{x})}{\color{blue}{(2-\sqrt{x})(2+\sqrt{x})}}\\
\textit{keeping in mind that }\color{blue}{(a-b)(a+b)} = (a^2-b^2)\)

Answer 6

Thanks guys, I think I got it