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Chapter 4: Q 16. (page 339)

Explain why the sum ${鈭�}_{k = 1}^{100} f (2 + 0.1 (k - 1)) (0.1)$ can't be a left sum for f on $[a, b] = [2, 5]$

Short Answer

Expert verified

Part of the sum denotes $0.25$ and the other part indicates $0.5$

Step by step solution

01

Step 1. Given information

Sum is ${鈭�}_{k = 1}^{100} f (2 + 0.1 (k - 1)) (0.1)$

02

Step 2. Explanation

Consider the sum ${鈭�}_{k = 1}^{100} f (2 + 0.1 (k - 1)) (0.1)$

${鈭�}_{k = 1}^{100} f (2 + 0.1 (k - 1)) (0.1) = f (2 + 0.1 (1 - 1)) (0.1) + f (2 + 0.1 (2 - 1)) (0.1) + f (2 + 0.1 (3 - 1)) (0.1) + . . .$

Part of it denotes 0.25 and other part denotes 0.5

So, the sum is incorrect.

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