lim_(x rarr2)(|x-2|)/(x-2)

lim_(x rarr2)[(x-2)/(x^(2)-4)-(1)/(x^(3)-3x^(2)+x)]=(1)/(m) where l and m are mutually prime then the value of (l+m)

Test the existance of the limit lim_(x rarr 2)[3|x-2|+(x-2)]/|x-2| ,x ne -2 .

Evaluate: lim_(x rarr2)(x^(2)-x-2)/(x^(2)-2x-sin(x-2))

lim_(x rarr2)(x-2)/(sqrt(x^(2)-4)+sqrt(x-2))

lim_(x rarr2)(x-2)/(sqrt(x+2)-sqrt(3x-2))

lim_(x rarr2)(x-2)/(sqrt(x)-sqrt(2))

Show that lim_(x rarr2)[(1)/(x-2)-(1)/(x^(2)-3x+2)]=

lim_(x rarr2)(x^(2)-2x)/(x^(3)-8)