Question

limit as (x to infinity) (root (x^2-20 x+3)-x) (Is LH really needed here? What value does a graph suggest?).

Answer 1

-10

Explanation:

`\displaystyle \lim_(x\rightarrow\infty)√(x^2-20x+3)-x\\\\=\lim_(x\rightarrow\infty)√(x^2-20x+100-97)-x\\\\=\lim_(x\rightarrow\infty)√((x-10)^2-97)-x\\\\=\lim_(x\rightarrow\infty)x-10-x\\\\=-10`