Let a1,a2,⋯,an be fixed real numbers and define a function f(x)=(x−a1)(x−a2)…(x−an)
What is limx→a1f(x)? For some a≠a1,a2….an compute limx→af(x).
Given : f(x)=(x−a1)(x−a2)⋯(x−an)
limx→a1f(x)=limx→a1(x−a1)(x−a2)⋯(x−an)
=(a1−a1)(a1−a2)⋯(a1−an)
=0×(a1−a2)⋯(a1−an)
=0
Hence, limx→a1f(x)=0