Question

The limit of the product of two functions equals the ____ of their limits.

Short answer

The limit of the product of two functions equals the product of their limits.

Step-by-step solution

Step 1. Given information

Fill in the blank statement:

The limit of the product of two functions equals the ____ of their limits.

Step 2. Limit of a Product theorem.

Limit of a Product:

$\underset{x\to c}{\lim }\left[f\left(x\right)·g\left(x\right)\right]=\left[\underset{x\to c}{\lim }f\left(x\right)\right]\left[\underset{x\to c}{\lim }g\left(x\right)\right]$

The limit of the Product theorem can be written in words as:

The limit of the product of two functions equals the product of their limits.