Question

What is the lim of (((1/x)-(1/2))/x-2) , as x approaches 2

Answer 1

I assume the denominator is
`x-2`.


`\lim_(x\to2)((1)/(x)-(1)/(2))/(x-2)=\\ \lim_(x\to2)((2)/(2x)-(x)/(2x))/(x-2)=\\ \lim_(x\to2)((2-x)/(2x))/(x-2)=\\ \lim_(x\to2)(2-x)/(2x(x-2))}=\\ \lim_(x\to2)-(x-2)/(2x(x-2))}=\\ \lim_(x\to2)-(1)/(2x)}=\\ -(1)/(2\cdot2)=\\ -(1)/(4)=`