In the following library of functions, what are the values of

for which

?

Polynomial function:

Rational function:

Trigonomic functions:

,

,

,

,

,

,

Exponential functions:

Natural logarithmic functions:

I just kind of threw this out there guys because I'd like to improve my understanding of limits and continuity. Anyone who wants to tackle these has a thanks coming. More than one person's views are always welcome, so if anyone sees that the questions already been answered, don't let that stop you putting your spin on it. Thanks guys.