Question #9c8b1

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Answer 1 · 2017-03-16T20:23:44

#x=+-oo

Given:#" "2/3x^(-2/3)=0#

Multiply both sides by 3/2

#x^(-2/3)=0#

THERE IS A TRAP IN THIS!!!!

It is tempting to say that #x=0# This is wrong!

#x^(-2/3)" is the same as " 1/(x^(2/3))#

Clearly #x!=0# as this is an excluded value in that #1/0# is 'not allowed'. However as #x->0# then #x^(2/3)->0" "# so #" "1/(x^(2/3))->oo#

So lets consider the other end of the 'number spectrum' instead of x=0 what about #x=oo#

In this condition we end up with #1/(x^(2/3)->oo)# which is so minute that it may as well be 0, but in this case it exists

So #2/3x^(-2/3)=0" "=>" "x=+-oo#

Tony B