# Tagged Questions

For questions about or involving the absolute value function.

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### absolute value inequality with complex number

Strangely, I don't find easily on the internet sources about inequalities with complex numbers. In this moment, I am interested to absolute value inequalities with complex numbers but would be good ...
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### Different way to solve $|x-3|<|2x|$

I know two ways I can solve $|x-3|<|2x|$ By squaring both sides By interpreting the inequality as a statement about distances on the real line. Question: How can I solve this inequality ...
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### Solve the equation within 'floor function'

I added my solution, but I'm not sure I've got it right. I'd like to know what you think. The question: Solve the equation: $$\lfloor |x+1|-|x| \rfloor \ge x^2.$$ the left and right symbols ...
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### Is it possible to find the absolute value of an integer using only elementary arithmetic?

Using only addition, subtraction, multiplication, division, and "remainder" (modulo), can the absolute value of any integer be calculated? To be explicit, I am hoping to find a method that does not ...
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### If $|ax^2+bx+c|\le 1\ \forall |x|\le 1$, then what is the maximum possible value of $\frac 83a^2+2b^2$? [closed]

Let $f(x) = ax^2 + bx + c$ ; $a,b,c\in\mathbb R$ It is given that $|f(x)| \le 1$ $\forall |x| \le 1$ Q1) The possible value of $|a+c|$, if $\displaystyle \frac{8}{3} a^2 + 2b^2$ is maximum, is ...
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### Is this a misprint or am I missing something?

What I'm given is this: Evaluate: x = 5, |x| -2 I'm thinking they probably mean |x|=-2, in which case the evaluation would be false. But then again I second ...
### Definition of limit with$f(x)=|x^3|$
Using the definition of the limit I tried to find the derivative of $f(x)=|x^3|$. I came up with: $$f'(x)=\frac{3x^5}{|x^3|}$$ Question: Why is the derivative (according to this answer) not defined ...