How do you prove that the limit #((x^2+x-6)/(x-2))=5# as x approaches 2 using the formal definition of a limit?

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Answer 1 · 2016-07-12T23:51:50

below

#lim_{x to 2} ((x^2+x-6)/(x-2))#

let #x = 2+h#

#= lim_{h to 0} (((2+h)^2+(2+h)-6)/((2+h)-2))#

#= lim_{h to 0} (4+4h+ h^2+2+h-6)/(h)#

#= lim_{h to 0} (5h+ h^2)/(h)#

#= lim_{h to 0} 5 + h#

#=5#