# absolute

1. ### absolute value and inequality problems

Inequalities and absolute value, Hello everyone, I have done the following questions and would just like to confirm that my answers are in deed correct. I'm a bit paranoid about them. 1) (y/x - x/y) / (5/y - 5/x) just simplify 2) Solve the inequality in terms of intervals: -1 < 2x - 5 < 7...
2. ### Critical Points

f(x) = |2x|-|x - 2| Are, x = 0 and x = 2, considered as Critical Points? --------------- Our doctor said that they are not, but I argued with him that they are Critical Points. --------------- Is his statement correct?
3. ### Absolute Extrema

Find the absolute extrema of the given function on each indicated interval. f(x) = |2x| - |x - 2| on (a) [0,1] and (b) [-3,4]
4. ### The Absolute Value of a Number

lim 5x/(x^2 + 9)^1/2 as x goes to -4 = -20/|5| The square root of 25 could be +5 or -5. How do I decide now if the absolute of 5 is positive or negative?
5. ### Is this statement true regarding squares and Absolute Value?

The following statement seems obvious to me, but I don't want to take it for granted. a^2 = {|a|}^2 for all real numbers a . Is this a theorem or definition, or is there already one out there that supports it? Thx...
6. ### Solving Systems of Equations with Absolute Value Operators

Suppose we have a line formula: Y = m * (X) (Eq. 1) where m is our slope and our y-intercept is zero. Let us assume that m is always positive. Now let us suppose that Y and X are actually functions of two hidden variables, P and Q. Y = |P + Q| (Eq. 2) X = (|P| + |Q|) /...
7. ### Absolute Value equation with only one solution ?

Hello , Is there more than one solution to this equation ? 2|3x+8|-3=5|x-1|+6 I came up with x=-12 or x=-30 but only -30 satisfies the equation , if this is correct , how come there is only one possible solution ? shouldn't there be two ? Here are the steps i took to reach said solutions ...
8. ### ratio test to test absolute convergence

in this question , i tried to solve it using ratio test to determine whether it is absolutely convergent or not , unfortunealy , i keep on getting infinity/ infinity , what does it mean ? does it mean diverge absolutely or ration test is not suitable to test the series ? if it is diverge...
9. ### Finding the domain of absolute convergence

Find the domain of absolute convergence for: $$\sum_{n=1}^\infty \frac{(n!)(iz+1)^n} {n^3+ \sqrt[3] {n}}$$ which test should be used in this case? I tried the ratio test, but the terms did not cancel out (some did): \$\lim_{n\to \infty} \frac{(n+1)!(iz+1)^{n+1}} {(n+1)^3 + \sqrt[3]...
10. ### Absolute value inequality

hello :) Answer: (2, 14/3)-{3} I would appreciate if you show me step by step!
11. ### limit of absolute values at infinity

Hello, I am having trouble with this limits question: Evaluate (abs(-x)+abs(3-x))/x as x tends to infinity I know the answer is 2 but I can't seem to solve it. It would be of great help if you could explain it step by step, I would greatly appreciate it!
12. ### Mean Absolute Value

Hi, I am finding a method for making sense of a stochastic (random) signal, such as the one shown in the attached picture. From the research that I have done, I found that the Mean Absolute Value method is used. This method consists of sampling the signal at a particular window frame, rectifying...
13. ### Range of Absolute Value Function

Find the range of y = |x + 4| without using a calculator or graphing.
14. ### Absolute Max and Min Problem

Find absolute max and min value or values of f on the set D. f(x,y) = x^{2} + y^{2} + x^{2}y + 9 D = {(x,y) | |x| \leq 1, |y| \leq 1} f_{x} = 2x - 2xy f_{y} = 2y + x^{2} f_{xy} = 2x f_{xx} = 2 + 2y 2x - 2xy = 0 (This is f_{x} set to 0)) 2x(1 - y) = 0 2x = 0 x = 0 2y +...
15. ### Derivative of Absolute Value Function

Find y ' for y = |(cos x)/(cos x - 1)| My answer is tan x + (sin x)/(cos x - 1). Book's a swer is - tanx + (sin x)/(cos x - 1). Question: Where did the minus sign come from? Why -tanx? Why not tan x?
16. ### Verify Absolute Value Equation

Math Time Given two real numbers a and b, the notation max(a, b) denotes the larger of the two numbers. For example, if a = 1 and b = 2, then the max(1, 2) = 2. In cases where a = b, then the max(a, b) denotes the common value of a and b. So, we can express the absolute value as follows...
17. ### Absolute Value of a Complex number

Hi, i've tried this multiple times and I still can't seem to get the answer, so basically the point I try to do is rationalize the denominator to a real number, then I use |a^2+b^2| formula. The answer is : 1
18. ### Absolute Value and Continuity

Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? f(x) = |x - 3|/(x - 3) I don' t know where to start.
19. ### Solve a less than inequality with absolute values on both sides

Hi! Wondering if anyone can help me with this problem: |x+1| <= |x-3| I've done the 3 cases approach, with the cases being: Case 1 Case 2 Case 3 x< -1 -1 <= x < 3...
20. ### Absolute Value Function

I like playing with derivatives. Here is a question I found online. Find the derivative of f(x). f(x) = |x + 4|/|x - 4| Now, what is the difference between the above function and the one below? f(x) = ln|x + 4|/ln|x - 4| I know the quotient rule is needed in both cases. To...