1. ### Find the set of points that satisfy:|z|^2 + |z - 2*i|^2 =< 10

Hello everyone, I've been struggling quite a bit with this problem, since I'm not sure how to approach it correctly. The inequality form reminds me of the equation of a circle (x^2 + y^2 = r^2), but I have no idea how to be sure about it. Would it help just to simplify the inequality in terms...
2. ### I Necessity of absolute value in Cauchy Schwarz inequality

Reading The Theoretical Minimum by Susskind and Friedman. They state the following... $$\left|X\right|=\sqrt {\langle X|X \rangle}\\ \left|Y\right|=\sqrt {\langle Y|Y \rangle}\\ \left|X+Y\right|=\sqrt {\left({\left<X\right|+\left<Y\right|}\right)\left({\left|X\right>+\left|Y\right>}\right)}$$...
3. ### Mathematical Analysis Proof: |x-y|<= |x|+|y|

Homework Statement 1. Show that for all real numbers x and y: a) |x-y| ≤ |x| + |y| Homework Equations Possibly -|x| ≤ x ≤ |x|, and -|y| ≤ y ≤ |y|? The Attempt at a Solution I tried using a direct proof here, but I keep getting stuck, especially since this is my first time ever coming...
4. ### Absolute value notation removal

Homework Statement Rewrite |x| < 1 and |x| > 1 by eliminating the absolute value sign Homework Equations |x| < 1 = -1 < x < 1 |x| > 1 = ? The Attempt at a Solution I know that |x| < 1 can be rewritten as -1 < x < 1 but I'm not sure about |x| > 1. Am I right to assume that |x| > 1 = -1 > x > 1?
5. B

### B Inequality of absolute values

Hi there, I'm having trouble understanding this math problem: |x| + |x-2| = 2 The answer says its: 0<=x<=2 I understand you need different "cases" in order to solve this. For example, cases for when x is less than 0, when x-2 is less than 0, etc. Thanks, blueblast
6. ### Epsilon distance between two terms

Homework Statement How close is x to x_0 (x_0 \neq 0) so that 2. Homework Equations The Attempt at a Solution I tried to use absolute value properties:- \epsilon \lt \frac{\sqrt{x_0^2+1}}{x_0^3} - \frac{\sqrt{x^2+1}}{x^3} \lt \epsilonBy adding in the three sides, we...
7. ### I Contradiction in an absolute value property?

An absolute value property is $$\lvert a \rvert \geq b \iff a\leq-b \quad \text{ or } \quad a\geq b,$$ for ##b>0##. Is this true for the case ##a=0##? I mean if ##a=0, \lvert a \rvert =0## so ##0 \geq b##. But ##b## is supposed to be ##b>0##, so we have a contradiction. How can this property...
8. ### Absolute value...

Homework Statement X and Y 2 real numbers / |x| <1 and |y|<1 Prove that |x+y|<|xy+1| Homework Equations The Attempt at a Solution |x+y|<2 I couldn't prove that |xy+1| >2 And couldn't find a way to solve the problem Please help
9. ### Separable differential equations

Homework Statement [/B] Homework Equations The Attempt at a Solution I've highlighted two equations on the screenshot. How did it proceed from the first to the second? I'm actually confused with the absolute values. What is the idea behind getting rid of the first absolute value(1-5v^2)...
10. ### Teacher told to set absolute value inequality to equal 0

So I was helping my sister on homework and there was this problem: 2 abs(2x + 4) +1 > or equal to -3 teacher told her to ignore the -3 and just set it equal to zero. Soo should you? This question got me confused. can't you just go about solving, bringing the 1 to the left and then dividing by 2...
11. ### For f(x) = abs(x^3 - 9x), does f'(0) exist

Homework Statement For f(x) = abs(x^3 - 9x), does f'(0) exist? The Attempt at a Solution [/B] The way I tried to solve this question was to find the right hand and left hand derivative at x = 0. Right hand derivative = (lim h--> 0+) f(h) - f(0) / h = (lim h--> 0+) abs(h^3 - 9h) / h...