Let:
$g(x)=\frac{1}{1+e^{1/(x-1)}}$
for $x\ne 1$ and $g(x)=a$ for $x=1$.
For what values of $a$ will $g(x)$ be continuous for every $x$?
Thanks in adavance!
Let:
$g(x)=\frac{1}{1+e^{1/(x-1)}}$
for $x\ne 1$ and $g(x)=a$ for $x=1$.
For what values of $a$ will $g(x)$ be continuous for every $x$?
Thanks in adavance!
Hint Look at $\lim\limits_{x\rightarrow1^+}g(x)$ and $\lim\limits_{x\rightarrow1^-}g(x)$ to determine what $a$ needs to be.