How do you evaluate #(x−4 )/ (x^2+6x−40)# as x approaches 4?

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Answer 1 · 2016-04-28T02:22:00

#lim_(xrarr4)(x-4)/(x^2+6x-40)=1/14#

Given,

#lim_(xrarr4)(x-4)/(x^2+6x-40)#

Factor the denominator.

#=lim_(xrarr4)(x-4)/((x+10)(x-4))#

Cancel the factors, #x-4# in the numerator and denominator.

#=lim_(xrarr4)color(red)cancelcolor(black)(x-4)/((x+10)color(red)cancelcolor(black)((x-4)))#

#=lim_(xrarr4)1/(x+10)#

Substitute #x=4#.

#=lim_(xrarr4)1/((4)+10)#

#=lim_(xrarr4)1/14#

#=1/14#