$\text{Let}$\lim_{x\to d}h(x)=P,$\lim_{x\to d}k(x)=Q\text{, and}$$h(x)\geq k(x)\text{ for all }x\text{ in an open interval containing }d.$ $\text{Show}$P\geq Q
$\text{This is what I tried to do:}$|h(x)-P|\leq\epsilon,$|k(x)-Q|\leq\epsilon,$ $-\epsilon\leq h(x)-P\leq\epsilon$ $-\epsilon\leq k(x)-Q\leq\epsilon$ $0\leq h(x)-k(x)-P+Q\leq0$ $|h(x)-k(x)-P+Q|=0\leq|h(x)-k(x)|+|P-Q|$ $\text{But I get stuck. What am I doing wrong?}$