Question

Let P be the partition of [a, b] then ||P|| is defined
as.​

Answer 1

Answer:

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Answer 2

Let P be the partition of [a, b] then ||P|| is defined as the maximum length of the subintervals into which [a, b] is divided by the partition P

Given :

P be the partition of [a, b]

To find :

||P|| is defined as

Solution :

Step 1 of 2 :

Find partition

Let [a, b] be a closed and bounded interval and P = ( a , x₁ , x₂ , x₃ , x₄ , . . . , b ) be a partition of [a, b]

Step 2 of 2 :

Define norm of the partition

The norm of the partition denoted by ||P|| and defined as

$\sf | |P| | = max \{( x_1 -a) ,( x_1 -x_0) ,...,( b -x_{n - 1}) \}$

Hence ||P|| is defined as the maximum length of the subintervals into which [a, b] is divided by the partition P

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