Unstructured boundary notation when it is in an exponent

Question

I’m having a hard time getting the function lim_{x to infty} to stay in the structured exponent so that {x to infty} is below and not on the 'Lim' side. This only happens when I limit the exponent.

e ^ { \lim_{x \to + \infty} \left(  { \ln \left( \dfrac{2x +3 }{2x + 1} \right) \  \cdot   \ x } \right)  }

The result is strange and difficult to understand.

(When you’re normal Remembering that it doesn’t happen When you’re on top- )

\lim_{x \to + \infty}  \left( e ^ { \ln \left( \dfrac{2x +3 }{2x + 1} \right) \  \cdot   \ x } \right)

Answer 1

Use \limits shortly after \lim:

e^{ \lim\limits_{x \to + \infty} \left( { \ln \left( \dfrac{2x +3 }{2x + 1} \right) \cdot   \ x } \right) }

Particularly, when the exponent is complicated like this, I prefer to use the notation \exp, but it’s all about style anyway:

\exp \left( \lim_{x \to + \infty} { \ln \left( \dfrac{2x +3 }{2x + 1} \right) \  \cdot   \ x } \right) }