# Questions tagged [absolute-value]

For questions about or involving the absolute value function.

295 questions
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### absolute values and integals

I have the following integral $$\int_{- \infty}^\infty e^{-|x|} dx$$ and the following two questions (1) Since the preimages $x$ determine the the images $e^{-|x|}$ for nonnegative and negative ...
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### Around an inequality

I have a very general question, hopefully not too general. Assume that we have real numbers $a_{ij}, b_{ij}$ $(1 \leq i, \: j \leq n)$ such that $-1 \leq a_{ij}, b_{ij} \leq 1$ for all $i,j,$ for ...
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### why and when t0 use norm instead of abs and vice versa

What is the difference between the norm and abs of an expression.. as far i understand does ||a - z|| mean norm and |a-z| abs , but what is the difference?
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### Solving $n \int_{\mathbb{R}}{\left|\frac{1}{n}\sum_{j=1}^n{e^{(itY_j)}}-e^{-\frac{1}{2}t^2}\right|^2}\psi(t)dt$

I have to solve $$n \int_{\mathbb{R}}{\left|\frac{1}{n}\sum_{j=1}^n{e^{(itY_j)}}-e^{-\frac{1}{2}t^2}\right|^2}\psi(t)dt$$ where $\psi(t)=(2\pi)^{-\frac{1}{2}}e^{-\frac{1}{2}t^2}$ is the density ...
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### How to Solve a System of Absolute Value Equations Algebraically

How can one find the points of intersections of the two graphs algebraically? $$f(x) = |(x-1)^2-4|$$ $$f(x) = |x+3|-2$$ I understand that it could be solved graphically and through some sort of ...