1.

1.998 < x < 2.002 Express in modulus and neighbourhood form

Answer»

Here, a – δ = 1.998; a + δ = 2.002
By adding, 2a = 4
∴ a = 2
Putting a = 2 in a + δ = 2.002,
δ = 0.002
In Modulus form: |x – a| < δ
Putting a = 2; δ = 0.002,
1.998 < x < 2.002 = |x – 2| < 0.002

In Neighbourhood form : N (a, δ)
Putting a = 2; δ = 0.002,
1.998 < x < 2.002 = N (2, 0.002)


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