Find limₓ→₁ f (x), where f(x) = {x² - 1, x ≤ 1 and (- x² - 1), x > 1}

Solution:

The given function is f (x) = {x² - 1, x ≤ 1 and (- x² - 1), x > 1}

Now,

limₓ→₁₋ f (x) = limₓ→₁ [x² - 1] (as x < 1)

= 1² - 1

= 1 - 1

= 0

limₓ→₁+ f (x) = limₓ→₁ [-x² - 1] (as x > 1)

= -1² - 1

= -1 - 1

= -2

It is observed that limₓ→₁₋ f (x) ≠ imₓ→₁+ f (x)

Hence the given limit limₓ→₁ f (x) does not exist

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NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 24

Find limₓ→₁ f (x), where f(x) = {x² - 1, x ≤ 1 and (- x² - 1), x > 1}

Summary:

limₓ→₁ f (x) does not exist where f(x) = {x² - 1, x ≤ 1 and (- x² - 1), x > 1}