How do you find the limit of #(1/x-1/2)/(x-2)# as #x->2#?

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Answer 1 · 2016-11-22T22:42:13

#lim_(x->2)(1/x-1/2)/(x-2)#

Simplify the equation:

#= lim_(x->2)((2-x)/(2x))/(x-2)#

#=lim_(x->2)(2-x)/((2x)(x-2))#

Manipulate the equation to simplify further:

#=lim_(x->2)(-(x-2))/((2x)(x-2))#

Cancel and solve:

#=lim_(x->2)(-1)/((2x))=-1/4#