Find limₓ→₅ f (x), where f (x) = |x| - 5

Solution:

The given function is f (x) = |x| - 5. 

To find the value of the given limit, we will calculate the left-hand and the right-hand side limits.

limₓ→₅₋ f (x) = lim_x→5^- [|x| - 5]

= limₓ→₅ (x- 5)     [When x > 0, |x| = x]

= 5 - 5

= 0

limₓ→₅₊ f (x) = lim_x→5⁺ [|x| - 5]

= limₓ→₅ (x - 5) [When x > 0, |x| = x]

= 5 - 5

= 0

We have

limₓ→₅₋ f (x) = limₓ→₅₊ f (x) = 0

Hence, limₓ→₅ f (x) = 0

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NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 27

Find limₓ→₅ f (x), where f (x) = |x| - 5

Summary:

The value of limit limₓ→₅ f (x) is 0