We know that
$\lfloor x\rfloor$ : greatest integer $\leq x$
$\lceil x\rceil$ : least integer $\geq x$
$\mathrm{frac}(x)=x-\lfloor x\rfloor$
I can solve the questions limit of function like $$ \lim\limits_{x\to n^\pm}\frac{\lfloor x-1\rfloor}{x-1}\\ \lim\limits_{x\to n^\pm}\frac{\lfloor x\rfloor}{x-1} $$ As $x$ approaches $n$ from above, $\lfloor x-1\rfloor=n-1$; therefore, $$ \lim_{\large x\to n^+}\frac{\lfloor x-1\rfloor}{x-1}=\frac{n-1}{n-1} $$ but I can't solve the questions like
$$ \lim\limits_{x\to\infty}\frac{\lfloor x-3\rfloor}{x-1},\\ \lim\limits_{x\to\infty}\frac{\lceil x-3\rceil}{x-1},\\ \lim\limits_{x\to a} \lfloor x\rfloor,\\ \lim\limits_{x\to a} \lceil x\rceil,\\ \lim\limits_{x\to a} \mathrm{frac}( x) $$ for $a\in \mathbf{R}$
All questions are similar type, so I have given many problems in my questions. Please help me.