Question #60d52

1 Answer
Jim S
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#

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