use a graph to find the following limit.\n\n$$\\lim _ { x \\rightarrow \\infty } e ^ { - 2 x }$$\n\n$$\\lim…

use a graph to find the following limit.\n\n$$\\lim _ { x \\rightarrow \\infty } e ^ { - 2 x }$$\n\n$$\\lim _ { x \\rightarrow \\infty } e ^ { - 2 x } = \\square$$\n(simplify your answer.)

use a graph to find the following limit.\n\n$$\\lim _ { x \\rightarrow \\infty } e ^ { - 2 x }$$\n\n$$\\lim _ { x \\rightarrow \\infty } e ^ { - 2 x } = \\square$$\n(simplify your answer.)

Answer

Explanation:

Step1: Rewrite the function

The function (e^{-2x}) can be rewritten as (\frac{1}{e^{2x}}).

Step2: Analyze the limit as (x\to\infty)

As (x\to\infty), (2x\to\infty). Then (e^{2x}\to\infty) (since the exponential function (y = e^{u}) with (u = 2x) and as (u\to\infty), (e^{u}\to\infty)). Since (e^{-2x}=\frac{1}{e^{2x}}), and (\lim_{x\to\infty}e^{2x}=\infty), we have (\lim_{x\to\infty}\frac{1}{e^{2x}} = 0) (because (\frac{1}{\text{very large number}}\to0)).

Answer:

(0)