Chapter 11, Problem 4CRQ

To determine

To fill: The blank in the statement “If $\underset{n\to \infty }{\lim }{a}_n=A,\underset{n\to \infty }{\lim }{b}_n=B$, and c is any real number, then $\underset{n\to \infty }{\lim }c{a}_n=\_\_\_\_\_,\underset{n\to \infty }{\lim }\left(a_n+b_n\right)=\_\_\_\_\_,\underset{n\to \infty }{\lim }{a}_n{b}_n=\_\_\_\_\_\_$, and $\underset{n\to \infty }{\lim }\frac{a_n}{b_n}=\_\_\_\_\_\_$, provided that _______”.