Is there a way to change the text size of \displaystyle?

Question

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 $\displaystyle\lim_{x\to c}g\ne0.$

Answer 1

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You have

$\displaystyle\lim_{x\to c}\left(\frac fg\right)=\frac{\displaystyle\lim_{x\to c}f}{\displaystyle\lim_{x\to c}g},$ provided $\displaystyle\lim_{x\to c}g\ne0.$

However it should be (compare the final dot):

$\displaystyle\lim_{x\to c}\left(\frac fg\right)=\frac{\displaystyle\lim_{x\to c}f}{\displaystyle\lim_{x\to c}g},$ provided $\displaystyle\lim_{x\to c}g\ne0$.

You want to either


$\lim_{x\to c}\limits\left(\frac fg\right)=\frac{\textstyle\lim_{x\to c}\limits f}{\strut\textstyle\lim_{x\to c}\limits g},$ provided $\lim_{x\to c}\limits g\ne0$.

or:


$\lim_{x\to c}\limits\left(\frac fg\right)=\frac{\lim_{x\to c}\limits f}{\lim_{x\to c}\limits g},$ provided $\lim_{x\to c}\limits g\ne0$.

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