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...
Reading The Theoretical Minimum by Susskind and Friedman. They state the following...
$$\left|X\right|=\sqrt {\langle X|X \rangle}\\
\left|Y\right|=\sqrt {\langle Y|Y \rangle}\\
\left|X+Y\right|=\sqrt {\left({\left<X\right|+\left<Y\right|}\right)\left({\left|X\right>+\left|Y\right>}\right)}$$...
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...
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?
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
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...
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...
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
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)...
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...
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...