Evaluate: `underset(xrarr2)"lim"(x^(2)-4)/(x-2)`

Evaluate underset( x rarr 2^+ ) ( "lim") ( x-2)/( sqrt( x^(2) -4) +sqrt(x - 2))

Consider the following statements: I. underset(xrarr0)lim (x^(2))/(x) exists. II. ((x^(2))/(x)) is not continuous at x = 0. III. underset(xrarr0)(lim)(|x|)/(x) does not exist Which of the above statements are correct?

Evaluate lim_(xrarr2){((x^(2)-4))/(sqrt(3x-2)-sqrt(x+2))}.

Evaluate: lim_(xrarr2) (x^(2)-4)/(x-2)

lim_(xrarr2) (x^(3)-8)/(x^(2)-4)

lim_(xrarr0) (x^(2)-x)/(sinx)

Evaluate the following limits and justify each step. underset(xrarr5) ( "Lim") ( 2x^(2)-3x+ 4)

Evaluate the following limits and justify each step. underset(xrarr -2) ( "Lim") ( x^(3)+2x^(2) -1)/(5-3x)

Evaluate: lim_(xrarr3) (x^(2)-4x+3)/(x^(2)+6x- 27)

Evaluate underset(x to -oo)lim(sqrt(x^(2)+3x+1))/(2x+4)