Chapter 9.4, Problem 10QR

To determine

Toshow: that the functions grow at the same rate as $x\to \infty$ .

Explanation of Solution

Given information:

Thefunctions are $f\left(x\right)=\sqrt{2x-1},g\left(x\right)=\sqrt{x+3}$

Proof: to show that the functions grow at the same rate, find the limit of these function ratio,

  $\underset{x\to \infty }{\lim }\frac{\sqrt{2x-1}}{\sqrt{x+3}}=\frac{2}{1}\text{ [simplify]}$

Because the limit of the ratio of function is constant,

Thus, the functions grows at the same rate.