What does (x^3-a^3)/(x^4-a^4) equal when the limiting factor is x approaches a? Thank you!!!

1 Answer
MattyMatty
Feb 8, 2018

#3/(4a)#

Explanation:

#(x^3 - a^3) = (x-a)(x^2+a x+a^2)#
#(x^4 - a^4) = (x^2-a^2)(x^2+a^2) = (x-a)(x+a)(x^2+a^2)#
#=> (x^3-a^3)/(x^4-a^4) = ((cancel(x-a))(x^2+a x+a^2))/((cancel(x-a))(x+a)(x^2+a^2))#
#"Now fill in x = a : "#
#= (3 a^2)/((2 a)(2 a^2))#
#= 3/(4a)#

#"We could also use the l' Hôpital rule :"#
#"Deriving numerator and denominator yields : "#
#"(3 x^2) / (4 x^3) = 3/(4x)#
#"Now fill in x=a : "#
#"= 3/(4a)#

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