Troubleshooting Homework: Identifying and Addressing Mistakes

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SUMMARY

This discussion focuses on troubleshooting a homework problem related to conservative fields and path independence in vector calculus. Participants emphasize the importance of recognizing that the integral of a gradient function (F = grad f) is central to solving the problem. A specific calculation is highlighted, where the expression (9 - 12 + 4) - (1/4 + 1 - 1) leads to a result of 3/4, contrasting with an incorrect answer of -27/4 found in the textbook. The key takeaway is that the solution requires completing the calculations accurately while applying the principles of conservative fields.

PREREQUISITES
  • Understanding of vector calculus concepts, specifically conservative fields
  • Familiarity with path independence in integrals
  • Knowledge of gradient functions and their integrals
  • Basic arithmetic and algebra skills for simplifying expressions
NEXT STEPS
  • Study the properties of conservative vector fields in depth
  • Learn about path independence and its applications in vector calculus
  • Review the integral of gradient functions and related theorems
  • Practice solving problems involving gradients and integrals
USEFUL FOR

Students studying vector calculus, educators teaching advanced mathematics, and anyone looking to enhance their problem-solving skills in conservative fields and integrals.

Shackleford
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Homework Statement



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Homework Equations



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The Attempt at a Solution



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You're right, it is a conservative field - that's the key to the solution.
I think you're trying to use path independence, which is also key, but try it another way.
you're looking for the integral of F; and F = grad f... well... what's the integral of grad f?
 
Actually, I can't really see a problem. So...am I really just that rusty? What's the answer supposed to be?
 
The only thing you are doing wrong is that you have not finished the problem!

You have (9- 12+ 4)- (1/4+ 1- 1). Okay, what number is that?
 
HallsofIvy said:
The only thing you are doing wrong is that you have not finished the problem!

You have (9- 12+ 4)- (1/4+ 1- 1). Okay, what number is that?

Well, that answer is 3/4, but the answer in the back of the review has -27/4.
 
lzkelley said:
You're right, it is a conservative field - that's the key to the solution.
I think you're trying to use path independence, which is also key, but try it another way.
you're looking for the integral of F; and F = grad f... well... what's the integral of grad f?

I have that written out.
 

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