How do you find the limit of # (x^7 + 8x^3)/(4x^8 + 6x^12)# as x approaches 0?

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Answer 1 · 2016-04-21T21:16:47

oo

#lim_(x->0)(x^7+8x^3)/(4x^8+6x^12)#

#lim_(x->0) (x^3(x^4 +8))/(x^3(4x^5+6x^9)#

#lim_(x->0) (x^4 +8)/(4x^5+6x^9)#

#=8/0 = oo#

Answer 2 · 2016-04-21T22:12:44

The limit does not exist.

Let #f(x) = (x^7+8x^3)/(6x^12+4x^8) = (x^4+8)/(6x^9+4x^5)#

#lim_(xrarr0^-)f(x) = -oo#

#lim_(xrarr0^+)f(x) = oo#

Therefore,

#lim_(xrarr0)f(x)# #" "# Does Not Exist.