I know you can apply different font sizes in math mode such as \scriptstyle and \scriptscriptstyle. What I am looking for is a way to get that "size" but still have the "style" of \displaystyle.
Specifically I am wanting to put limits in the numerator and denominator of a fraction, and the \displaystyle makes the expressions nearly overrun the fraction bar. Here's the code I am using...
$\displaystyle\lim_{x\to c}\left(\frac fg\right)=\frac{\displaystyle\lim_{x\to c}f}{\displaystyle\lim_{x\to c}g},$ provided $\displaystyle\lim_{x\to c}g\ne0.$

\displaystyleand use\lim\limits_{...– David Carlisle Jul 29 '15 at 15:41