Question #60d52

1 Answer
Jan 9, 2018

Diverges

Explanation:

lim_(xrarr3)(1/(x^2-9)-1/(x^3-27)) =

lim_(xrarr3)(1/(x^2-3^2)-1/(x^3-3^3)) =

lim_(xrarr3)(1/((x-3)(x+3))-1/((x-3)(x^2+3x+9))) =

lim_(xrarr3)(x^2+3x+9-(x+3))/((x-3)(x+3)(x^2+3x+9)) =

lim_(xrarr3)(x^2+3x+9-x-3)/((x-3)(x+3)(x^2+3x+9)) =

lim_(xrarr3)(x^2+2x+6)/((x-3)(x+3)(x^2+3x+9))

If you replace for x=3 you get to the a/0 form

  • If x>3 , x->3^+

lim_(xrarr3^+)(x^2+2x+6)/((x^2-9)(x^2+3x+9)) =+oo

  • If x<3 , x->3^-

lim_(xrarr3^-)(x^2+2x+6)/((x^2-9)(x^2+3x+9)) =-oo