Question

Which of the following functions grows the fastest as x goes to infinity? (answer choices in pic file below)

Answer 1

out of these graphs, which one moves towards infinty on the right the most?

Answer 2

\[\frac{d}{dx}3^x=\frac{d}{dx}e^{x\ln3}=(\ln3)3^x\\
\frac{d}{dx}e^x=e^x\\
\frac{d}{dx}\ln x=\frac{1}{x}\\
\frac{d}{dx}x^3=3x^2\]
Is it clear that
\[\frac{1}{x}\leq 3x^2\leq e^x\leq (\ln3)3^x~~?\]