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LindseyM2011
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In equations dealing with absolute value sometimes the answer to the equation does not coorospond with the absolute value. Why is this?
Why Do Solutions Sometimes Differ from Absolute Values?
- Thread starter LindseyM2011
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Solutions to equations involving absolute values can differ from the expected absolute values due to the nature of absolute value itself, which represents the distance from zero on a number line. For example, the absolute value of -4 is 4, indicating its distance from zero, not its original value. This discrepancy occurs because absolute value equations can yield multiple solutions, especially when considering both positive and negative roots. Understanding absolute value requires recognizing that it simplifies to a non-negative result, regardless of the input's sign. Therefore, the solutions to these equations reflect this fundamental property of absolute values in mathematics.
Hello!
In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way:
I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true?
And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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