1.95 < x < 2.05 Express in modulus and neighbourhood form

1.	1.95 < x < 2.05 Express in modulus and neighbourhood form
Answer» Here, a – δ = 1.95; a + δ = 2.05 By adding, 2a = 1.95 + 2.05 = 4 ∴ a = 2 Putting a = 2 in a + δ = 2.05, δ = 0.05 In Modulus form: \| x – a \| < 8 Putting a = 2; δ = 0.05, 1.95 < x < 2.05 = \|x – 2\| < 0.05 In Neighbourhood form : N (a, δ) Putting a = 2; δ = 0.05, 1.95 < x < 2.05 = N (2, 0.05)

Answer»

Here, a – δ = 1.95; a + δ = 2.05
By adding, 2a = 1.95 + 2.05 = 4
∴ a = 2
Putting a = 2 in a + δ = 2.05,
δ = 0.05

In Modulus form: | x – a | < 8
Putting a = 2; δ = 0.05,
1.95 < x < 2.05 = |x – 2| < 0.05

In Neighbourhood form : N (a, δ)
Putting a = 2; δ = 0.05,
1.95 < x < 2.05 = N (2, 0.05)

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