Recall the result in part (a); lim x → 2 x − 2 x 2 − 2 x = 1 2 {\textstyle \displaystyle \lim _{x\to 2}{\frac {x-2}{x^{2}-2x}}={\frac {1}{2}}} .
Although g ( x ) = x 2 − 2 x = x ( x − 2 ) {\displaystyle g(x)=x^{2}-2x=x(x-2)} vanishes at x = 2 {\displaystyle x=2} , i.e., g ( 2 ) = 0 {\displaystyle g(2)=0} , the limit exists.
Therefore, the answer is F a l s e {\displaystyle \color {blue}False} .
