Question

How do you show the limit does not exist limx→4x−4x2−8x+16lim_(x->4)(x-4)/(x^2-8x+16) ?

Answer 1

`\lim\limits_(x\to4)(x-4)/(x^2-8x+16)=\lim\limits_(x\to4)(x-4)/((x-4)^2)=\lim\limits_(x\to4)(1)/(x-4)\\\\\lim\limits_(x\to4^-)(1)/(x-4)=(1)/(0^-)=-\infty\\\\\lim\limits_(x\to4^+)(1)/(x-4)=(1)/(0^+)=\infty`