Chapter 9.4, Problem 9QR

To determine

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

Explanation of Solution

Given information:

Thefunctions are $f\left(x\right)=4e^x-5,g\left(x\right)=3e^x+7$

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

  $\underset{x\to \infty }{\lim }\frac{4e^x-5}{3e^x+7}=\frac{4}{3}\text{ [simplify]}$

Because the limit of the ratio of function is constant,

Thus, the functions grows at the same rate.