Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### 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 \( \sum_{i=1}^{n} \Delta x_i \). --- **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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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 \( \sum_{i=1}^{n} \Delta x_i \). --- **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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