Question

1.Which of the following functions grows the fastest as x goes to infinity? (4 points)2xln(x)sin(x)x20

Answer 1

x^20

Step-by-step explanation:

To know which function grows the fastest as x goes to infinity, we need to replace x with great values.

For example, for x = 20 we get

`\begin{gathered} 2^x=2^(20)=1,048,576 \\ ln(x)=ln(20)=2.99 \\ sin(x)=sin(20)=0.34 \\ x^(20)=20^(20)=1.04*10^(26) \end{gathered}`

We get the grater value with x^20, so the function that grows the fastest is x^20