If the function f (x) satisfies limₓ→₁ (f (x) - 2) / (x² - 1) = π, evaluate limₓ→₁ f (x)

Solution:

It is given that the function f (x) satisfies the limit limₓ→₁ (f (x) - 2)/(x² - 1) = π

⇒ (limₓ→₁ f (x) - 2) / (limₓ→₁(x² - 1)) =π

⇒ limₓ→₁ (f (x) - 2) = π limₓ→₁ (x² - 1)

⇒ limₓ→₁ (f (x) - 2) = π (1² - 1)

⇒ limₓ→₁ (f (x) - 2) = 0

⇒ limₓ→₁ f (x) - limₓ→₁ 2 = 0

⇒ limₓ→₁ f (x) - 2 = 0

⇒ limₓ→₁ f (x) = 2

Hence, limₓ→₁ f (x) = 2

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 31

If the function f (x) satisfies limₓ→₁ (f (x) - 2) / (x² - 1) = π, evaluate limₓ→₁ f (x).

Summary:

If the function f (x) satisfies limₓ→₁ (f (x) - 2) / (x² - 1) = π, then limₓ→₁ f (x) = 2