Chapter 14.2, Problem 1AYU

To determine

To complete: The sentence “The limit of the product of two functions equals the ___ of their limits”.

Answer to Problem 1AYU

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

Explanation of Solution

Consider the Product Rule of Limits of two functions $f\left(x\right)$ and $g\left(x\right)$ .

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

So, the limit of the product of any two functions is the product of the limit of the two functions.