What is the limit of #(4x)/(x-6)+(5x)/(x+6)# as x approaches infinity?

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Answer 1 · 2016-03-18T12:09:13

The limit is #9#

#lim_(xrarroo)(4x)/(x-6) = lim_(xrarroo)(4x)/(x(1-6/x)) #

# = lim_(xrarroo)(4)/((1-6/x)) = 4/(1-0) = 4#

And

#lim_(xrarroo)(5x)/(x+6) = lim_(xrarroo)(5x)/(x(1+6/x)) #

# = lim_(xrarroo)(5)/((1+6/x)) = 5/(1+0) = 5#

Therefore,

#lim_(xrarroo)((4x)/(x-6) + (5x)/(x+6)) = lim_(xrarroo)(4x)/(x-6) + lim_(xrarroo)(5x)/(x+6) #

# = 4+5=9#