Question

Determine whether the integral ∫0[infinity]​e−2xdx converges or diverges.

Answer 1

The integral ∫0 to infinity (e^(-2x)dx) converges.

Step-by-step explanation:

The integral ∫0 to infinity (e^(-2x)dx) converges. To determine convergence or divergence of this integral, we need to evaluate the limit as the upper bound of integration approaches infinity. We can do this using the limit test.

Using the limit test, we have:

lim x→∞ (e^(-2x)) = 0

Since the limit is equal to zero, the integral converges.