How do you find the limit of #(1/(x+4)-(1/4))/(x)# as #x->0#?

1 Answer
mason m
May 2, 2017

#-1/16#

Explanation:

Find a common denominator within the fractions of the numerator:

#lim_(xrarr0)(1/(x+4)-1/4)/x=lim_(xrarr0)(4/(4(x+4))-(x+4)/(4(x+4)))/x#

#=lim_(xrarr0)(4-(x+4))/(x(4(x+4)))=lim_(xrarr0)(-x)/(4x(x+4))#

#=lim_(xrarr0)(-1)/(4(x+4))#

Now the limit can be evaluated since the #x# has been removed from the denominator:

#=(-1)/(4(0+4))=-1/16#

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