Mathematics

Problem

73. Prove that

\lim _{x \rightarrow-\infty} \frac{c}{1+a \cdot b^{x}}=0

and

\lim _{x \rightarrow \infty} \frac{c}{1+a \cdot b^{x}}=c

, for constants

a, b

, and

c

, with

a>0,0<b<1

and

c>0