Understanding 3 Digits of Accuracy in Calculus Problems

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In summary, the conversation is about a problem with finding the value of limits in calculus and the confusion over the use of "3 digits of accuracy." The speaker believes that 3 significant digits should be sufficient, but the phrase may be referring to 3 decimal places. They suggest that the wording could have been clearer to avoid confusion.
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afr123
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I'm refreshing my knowledge of calculus and ran into this problem while working on limits.

"Find∗ the value of each of the indicated limits to at least 3 digits of accuracy by evaluating f(x) at various values, or state that the limit does not exist (DNE)."

My problem is with "at least 3 digits of accuracy." If I type in an answer like 6.78, it says I'm wrong. If I type in the answer 6.778, it says I'm right. 6.78 has 3 significant digits though, so shouldn't that work?

It doesn't say 3 digits after the decimal point, it says "3 digits of accuracy." Isn't that referring to having 3 significant digits?
 
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IMO they are being sloppy by saying "digits of accuracy." To be clearer they should have phrased it as "three decimal places."
 
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Related to Understanding 3 Digits of Accuracy in Calculus Problems

What is the significance of 3 digits of accuracy in calculus problems?

The number of digits of accuracy in a calculation represents the precision or level of detail in the solution. In calculus, 3 digits of accuracy means that the answer is correct up to the third decimal place.

How do I determine the number of digits of accuracy in a calculus problem?

To determine the number of digits of accuracy, count the number of significant figures in the given values and the final answer. The number of digits in the final answer should match the number of significant figures in the given values.

Why is it important to have 3 digits of accuracy in calculus problems?

In calculus, having 3 digits of accuracy allows for more precise calculations and a better understanding of the behavior of functions. It also helps to avoid rounding errors and ensures the accuracy of the solution.

What are some common mistakes that can lead to incorrect digits of accuracy in calculus problems?

One common mistake is not following the correct order of operations, which can lead to incorrect calculations and therefore, an incorrect number of digits of accuracy. Another mistake is not paying attention to significant figures and rounding the final answer to the wrong number of digits.

Can the number of digits of accuracy in calculus problems ever be greater than 3?

Yes, the number of digits of accuracy can be greater than 3 if the problem requires a more precise answer. This is especially true in real-world applications where a higher level of accuracy is necessary. However, in most calculus problems, 3 digits of accuracy is sufficient.

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