Let a₁, a₂, ...., aₙ be fixed real numbers and define a function
f (x) = ( x - a₁)( x - a₂)....( x - aₙ).
What is limₓ→ₐ₁ f (x) ? For some a ≠ a₁, a₂, ...., aₙ, compute limₓ→ₐ f (x).

Solution:

The given function is f (x) = ( x - a₁)( x - a₂)....( x - aₙ)

We will evaluate the given limits now.

limₓ→ₐ₁ f (x) = limₓ→ₐ₁ [( x - a₁)( x - a₂)....( x - aₙ)]

= (a₁ - a₁)(a₁ - a₂) .... (a₁ - aₙ)

= 0

Now,

limₓ→ₐ f (x) = limₓ→ₐ [( x - a₁)( x - a₂)....( x - aₙ)]

= (a - a₁)(a - a₂) .... (a - aₙ)   [None of these are zero as a ≠ a₁, a₂, ...., aₙ]

Thus, limₓ→ₐ f (x) = (a - a₁)(a - a₂) .... (a - aₙ)

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 29

Let a₁, a₂, ...., aₙ be fixed real numbers and define a function f (x) = ( x - a₁)( x - a₂)....( x - aₙ). What is limₓ→ₐ₁ f (x) ? For some a ≠ a₁, a₂, ...., aₙ, compute limₓ→ₐ f (x).

Summary:

We found that limₓ→ₐ₁ f (x) = 0 and the value of limit limₓ→ₐ f (x) = (a - a₁)(a - a₂) .... (a - aₙ)