Determine if the following statement is true or false. n If a piece of string has been chopped into n small pieces and the ith piece is Ax, inches long, then the total length of the string is exactly Ax Choose the correct answer below Axi +1-AX₁ n h→0 i=1 OA. The statement is false. The length of the string is lim - h n OB. The statement is false. The length of the string is Σx₁. i=1 OC. The statement is false. This is only an approximation of the length, not the exact length. D. The statement is true O E. The statement is false. The length of the string is AX-AX₁|- n OF. The statement is false. The length of the string is Σ Ax₁ i=0 i=1
Determine if the following statement is true or false. n If a piece of string has been chopped into n small pieces and the ith piece is Ax, inches long, then the total length of the string is exactly Ax Choose the correct answer below Axi +1-AX₁ n h→0 i=1 OA. The statement is false. The length of the string is lim - h n OB. The statement is false. The length of the string is Σx₁. i=1 OC. The statement is false. This is only an approximation of the length, not the exact length. D. The statement is true O E. The statement is false. The length of the string is AX-AX₁|- n OF. The statement is false. The length of the string is Σ Ax₁ i=0 i=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Determine if the following statement is true or false.
If a piece of string has been chopped into \( n \) small pieces and the \( i \)th piece is \( \Delta x_i \) inches long, then the total length of the string is exactly \( \sum_{i=1}^{n} \Delta x_i \).
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**Choose the correct answer below.**
- **A.** The statement is false. The length of the string is \( \lim_{h \to 0} \sum_{i=1}^{n} \frac{\Delta x_{i+1} - \Delta x_i}{h} \).
- **B.** The statement is false. The length of the string is \( \sum_{i=1}^{n} x_i \).
- **C.** The statement is false. This is only an approximation of the length, not the exact length.
- **D.** The statement is true.
- **E.** The statement is false. The length of the string is \( |\Delta x_n - \Delta x_1| \).
- **F.** The statement is false. The length of the string is \( \sum_{i=0}^{n} \Delta x_i \).
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