In unicode-math, you can use the command
\setoperatorfont\mathsf
Otherwise, you can use code like egreg’s here to set the \operator@font to \sfdefault:
\documentclass{article}
\usepackage{amsmath}
\DeclareSymbolFont{sansops}{OT1}{\sfdefault}{m}{n}
\SetSymbolFont{sansops}{bold}{OT1}{\sfdefault}{b}{n}
\makeatletter
\renewcommand\operator@font{\mathgroup\symsansops}
\makeatother
\begin{document}
[ f(t) = a \sin (-t) + b \cos(-t) + c \sinh(t) + d \cosh (t) + k \exp (t) ]
\end{document}

For most documents, OT1 encoding will work. If you need accented Latin letters, but not uppercase Greek, you can change the legacy encoding from OT1 to T1. If you need lowercase Greek, you will need to find a sans-serif font that comes in the OML encoding.
MWE, there are many ways to achieve the request, belowDavislorsuggested method will works inXeLaTeXandLuaLaTeX– MadyYuvi Jul 09 '21 at 05:46\operatorname{\sf lim}– user313032 Jul 10 '21 at 14:44\sfhas been deprecated since 1993.\mathsf{lim}would do. – egreg Jul 10 '21 at 19:41\operatorname{\mathsf{lim}}works as well! Thanks! – user313032 Jul 10 '21 at 20:18