Evaluate limₓ→₀ f (x), where f (x) = {|x|/x, x ≠ 0 and 0, x = 0}

Solution:

The given function is f (x) = {|x|/x, x ≠ 0 and 0, x = 0}

Now,

limₓ→₀₋ f (x) = limₓ→₀₋ [|x|/x]

= limₓ→₀ (- x/x) [When x is negative, |x| = - x]

= limₓ→₀ (- 1)

= - 1

limₓ→₀₊ f (x) = limₓ→₀₊ [|x|/x]

= limₓ→₀ [x/x] [When x is positive, |x| = x]

= limₓ→₀ (1)

= 1

It is observed that limₓ→₀₋ f (x) ≠ limₓ→₀₊ f (x)

Hence, the given limit limₓ→₀ f (x) does not exist

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NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 25

Evaluate limₓ→₀ f (x), where f (x) = {|x|/x, x ≠ 0 and 0, x = 0}

Summary:

limₓ→₀ f (x) does not exist, where f (x) = {|x|/x, x ≠ 0 and 0, x = 0}