Question

Question 29 Let a1, a2, ...., an be fixed real numbers and define a function

f(x) = (x-a1) (x-a2)...(x-an)

What is lim(x-->a1) f(x)? For some a ≠ a1, a2...,an, compute lim(x-->a) f(x).

Class XI - Limits and Derivatives Page 303

Answer 1

lim (x→a1) = (a1-a1)(a1-a2)(a1-a3)...........(a1-an)
=> 0

now lim (x→a) = (a-a1)(a-a2)(a-a3)........(a-an) ≠0

for a ≠ a1, a2...,an