Two-Decimal Place Accuracy: Sum & Integral Solution

In summary, the conversation discusses the solution to a problem involving inequality, infinite summation, and improper integral. The solution uses a lower Riemann sum for the area represented by the integral. The individual also has a question about two-decimal place accuracy and why the error is stated as less than rather than less than or equal to. The response explains that the picky bit is just to ensure the correct rounding and is not as important as the first point about the Riemann sum.
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Homework Statement


The problem along with its detailed solution are attached.


Homework Equations


Inequality, infinite summation and improper integral.


The Attempt at a Solution


I'm following the solution but I can't justify the first (and only) less-than-or-equal sign. Why is that sum less-than-or-equal to that integral?

Also, to be picky, when they say two-decimal place accuracy, shouldn't that mean error <= 5/10^3 instead of error < 5/10^3? Whether I am right or wrong, please tell me why.

Any input would be greatly appreciated!
Thanks in advance!
 

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  • #2


The sum is a lower Riemann sum for the area represented by the integral. Draw a picture that shows why. The picky bit is just to guarantee you don't get an answer like 0.025 and round off the wrong way. It's much less important than the first point.
 
Last edited:

Related to Two-Decimal Place Accuracy: Sum & Integral Solution

1. How do you define two-decimal place accuracy?

Two-decimal place accuracy refers to the level of precision in a numerical value, where only the first two digits after the decimal point are considered significant. This means that any additional digits after the second decimal place are rounded or truncated.

2. What is the significance of achieving two-decimal place accuracy in scientific calculations?

In scientific calculations, achieving two-decimal place accuracy ensures that the results are precise and reliable. It allows for a better understanding and interpretation of data, and reduces the chances of errors in calculations.

3. How is two-decimal place accuracy calculated in a sum?

In a sum, two-decimal place accuracy is achieved by rounding the result to the nearest hundredth. This means that the third decimal place is rounded to the second decimal place, and any subsequent digits are dropped. For example, if the sum is 3.567, the two-decimal place accuracy would be 3.57.

4. What is the role of two-decimal place accuracy in integral solutions?

In integral solutions, two-decimal place accuracy ensures that the area under a curve is accurately measured. This allows for more precise calculations and interpretations of data, especially in scientific and mathematical contexts.

5. How can one check for two-decimal place accuracy in a result?

One can check for two-decimal place accuracy by verifying if the first two digits after the decimal point are significant and the remaining digits are either rounded or truncated. Additionally, one can use a calculator or perform the calculation manually to confirm the accuracy of the result.

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