Absolute value Definition and 365 Threads

Homework Statement Prove: |ab|=|a||b|. (Hint: Consider the cases separately for various signs of a and b.) Homework Equations I think it asks me to prove it only from the definition of absolute value (if it is possible). The Attempt at a Solution |ab|= \frac{(ab), if (ab)\geq0}{-(ab), if...

Homework Statement f(x) = |x+2|^3 -1 The Attempt at a Solution - So, I know the formula is: d|x| / dx = x / |x| - My guess would be: (x+2)^3 / |x + 2|^3 ? I'm trying to find Increase and Decrease intervals for the graph..

Homework Statement I just need to know if what i did is correct. The question is as follows: http://imgur.com/1RL7e Homework Equations The Attempt at a Solution What I did is as follows: I split this integral into two parts and solved. [integral from 0 to 1...

Homework Statement integrate modulus of xcos∏x within the limits -1 to 1/2 P.S I'm not allowed to use acaluculator so graphing and finding out the answer not possible Homework Equations it's using the property of definite integral ∫f(x) dx within the limit from a to b = ∫f(x) dx...

Homework Statement Determine the domain and find the derivative f(x) = ln|(x+2)/(x3 - 1)| Homework Equations The Attempt at a Solution We can factor x3 - 1 = (x-1)(x2) + x + 1) From this we know that x ≠ 1 or -2 because 1 would be undefined at -2 would cause the function to...

I need to find the absolute value of b(t): b(t)=a(t)[1+e^{-j2\pi tT}] Here is the answer in the textbook: \therefore \left | b(t) \right |=\left | a(t) \right |\sqrt{2(1+cos(2\pi tT)}2|cos(\pi tT)| However I got a different answer when working it out, and can't understand how they got...

Homework Statement I was helping my sister with her high school geometry homework, and she had to graph the absolute value function y=lx+6l using two linear equations. The way i did it was different than the way her book showed. Basically, I told her that when removing the absolute value you...

Hi All, I am confused about what is meant in the mathematical definition for the energy of a signal. Why is it the integral of the magnitude of the signal squared? ∫(|f(t)|^2) How do I deal with the absolute value sign? I do not have much experience with absolute value signs in...

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→−8 [ 8 − |x| OVER 8 + x ] The attempt at a solution First → abs(x) = -x ; x<0 / x ; x≥0 Therefore, our equation is going to look like 8 − -x OVER 8 + x If approaching -8 from the left, I...

hey~ folks! i'm in trouble with this integral problem. the range of the integral is from -∞ to ∞ and it has x as independent value. and the integrand is a derivative of absolute value in exponential; ∫^{∞}_{-∞} (d/dx e^{-a|x|})dx any idea for the problem??

absolute value help ... i am a bit confused about two things... first: is sqrt(x^2) is the same thing as |x|? if yes then consider a negative no. 'z' ... i had a question like this: sqrt(z^2)...its answer was -z...so i suppose this means that this square root/ square and absolute value thing...

Absolute value Quest, urgent Homework Statement a) |x-2| + |6-3x| = 12x Homework Equations The Attempt at a Solution I have a question about y this negetive becomes a positive.. :: Steps :: |x-2| + -3|x-2| |x-2| +3 |x-2| = 12x > this step if i factored out...

I saw some books and say that norm is the absolute value in vector. If it also means absolute value, why don't we use absolute value |\vec{v}| instead we use ||\vec{v}||?

I'm a little confused about solving absolute value equations and why sometimes solutions don't seem to make sense. Take a look at case (ii) on this website: http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_AbsoluteValueEquations.xml I understand the process of solving the...

Urgent! Absolute value help Homework Statement Heres an example :: |5x-3| = |x+1| we were given 3 cases for this type of problem in class they went something like this:: c.1 ) Use the 0 value for the right side and change all values in respect to (introduce - to all values) (x <...

Homework Statement |2x-8| + |12 - 3x | = 0 Homework Equations what do i do when it = 0 The Attempt at a Solution I tried solving it like all the others, but i know there is a unique thing to do when it = 0, i jus don't know what. So , here's what i did. 2|x-4| +...

Integral of 1/x = ln(x)... Problem has missing absolute value!? This is an ODE problem and solution, but what I'm not understanding here is calculus based: Why does the argument to the red-boxed ln() not in absolute value signs?? ( | | ) u = cos(t) so the numerator can be negative. I am just...

Homework Statement lim as x\rightarrow-1 = \frac{|x^{2}-1|}{x^{2}+x} Homework Equations N/a The Attempt at a Solution Tried to write this as a piecewise function, but I got lost.

Hi! Homework Statement I'm trying to work out this integral, without success: \int_{-a}^{a} (1-\left|x\right|/a) \frac{d^2}{dx^2}(1-\left|x\right|/a) 2. The attempt at a solution I tried solving this by parts, but I'm stuck: \int_{-a}^{a} (1-\left|x\right|/a)...

The following matrix problem occurred to me. I figured out the answer and would like to pose the problem. It's easy but would be best for an undergrad math major. The question: Consider a square n by n matrix with entries 1, 2, ..., n squared. Find a way to arrange these entries so that the...

Homework Statement Solve the equation | | 3x + 1 | - x | = 2 Homework Equations |x| = x if x \geq 0 |x| = -x if x < 0 The Attempt at a Solution To start, I have never dealt with such an equation before, and am partly 'iffy' with absolute values in general, but, up...

Homework Statement y = ln | sin x | Homework Equations - The Attempt at a Solution No attempt at a solution, because it's more of a "which part of this is incorrect" question. y = ln | sin x | Would everyone agree that this is equivalent? y = ln \sqrt{(sin x^2)} Then...

Homework Statement ∫ |x^2 -9| [0-4] Homework Equations The book answer states the same EXCEPT splits into [0-3] and [3-4]. Other problems split the integral perfectly in half for absolute values...why would it differ and are there rules to figure this out? Larson's Calculus has no...

Homework Statement Find all x in |5x-2| = 6x-12 The Attempt at a Solution http://www.wolframalpha.com/input/?i=Plot[|5x-2|+%3D+6x-12%2C{x%2C-1.5%2C1.5}] Notice how only x = 10 is a solution? So my question is, why isn't x = -14/11 a solution? I mean sure they don't...

[b]1. | (2-i)(3+2i)(-5-6i)(-7+3i) / (-4+i) | Homework Equations [b]3. I am pretty sure I am not computing it right but this is what i come up with. square root of 5* square root of 13* square root of 61* square root of 58 / square root of 17.

Homework Statement DIRECTIONS: Express the intercal in terms of an inequality involving absolute value. PROBLEM: (-4, 4) MY STEPS: 1: (-4, 4) 2: -4<x<4 3: |x|< 4 MY ANSWER Is that correct? Is step 3 correct? The only reason that I included that part is becuase it says...

Homework Statement Very embarrassing that I had problems with this. I managed to solved it at the end, but I am posting this for two reasons 1) I like someone else to work it out in a different method, I wnt to see what other approaches there are 2) Whether mine is taking too long or not. I...

Hi, I have a general question regarding the integrating factor of first-oder linear DEs. All textbooks that I've seen (which aren't too many) simply drop the absolute symbol when the factor has the form exp(ln(abs(x))). This would evaluate to abs(x), yet the books use simply x. Why is that...

Homework Statement If the absolute value of a sequence, an converges to absolute value of A, does sequence, an necessarily converge to A? Homework Equations convergence: a sequence { an}n=1-->infinity, converges to A є R (A is called the limit of the sequence) iff for all є > 0, there...

Homework Statement Let R be a set of real numbers derived from rational numbers. And, let R* be a set consisting of all ordered pairs of the form (x,0) where x is an element of R. For a complex number z = (a,b) = a+ib, I've learned that the absolute value of z is the number...

Homework Statement [PLAIN]http://img845.imageshack.us/img845/1706/delta.png The Attempt at a Solution This question has come after a chapter on Dirac's delta-function although the question doesn't say use it. Could I use it? If not how do I do it directly?

Homework Statement solve for x: 5|7-3x|+2=4|7-3x|-1 Homework Equations The Attempt at a Solution 7-3x>0 -3x>-7 x<3/7 {x|x<3/7} quantity is positive {x|x>3/7} quantity is negative I have never solved an equation with more than one absolute value quantity in it and am not sure how to start...

Homework Statement I was trying to show that 1) |a+b|≤|a|+|b| 2) |a+b|≥|a|-|b| and find out how they were true when a,b>0, a,b<0, and a>0,b<0 Homework Equations 1) |a+b|≤|a|+|b| 2) |a+b|≥|a|-|b| The Attempt at a Solution For |a+b|≤|a|+|b| a,b>0 I got that |a+b|=a+b...

Homework Statement just a simple problem as an example dy/dx = y/x dy/y = dx/x Homework Equations The Attempt at a Solution dy/y = dx/x ln|y| = ln|x| + c then when I take exponents do I still have to include the absolute value bar |y| = |x|c

Hello friends, I am quite confused how an absolute function is called a continuous one. f(x) = |x| has no limit at x=0 , that is when x > 0 it has a limit +1 {+.1, +.01, +.001} and -1 when x <0 {-.1, -.01, -.001} that is the reason it's not differentiable (left and right side limits are not the...

Homework Statement Im getting very confused with working out how to integrate the following double integral with an absolute value: \int^{2}_{-2}\int^{2}_{-2}\left|x^{2}+y^{2}-1\right|dxdy Homework Equations The Attempt at a Solution I know you have to split it down into where it...

Quick question (hopefully): I'm helping my girlfriend with some calculus homework over the phone and it looks like the book has a different answer for the derivative of an absolute value than I'm seeing in other places. I'm seeing it as (and I derived it myself to be) x/abs(x) whereas the book...

Homework Statement Prove that, if f is continuous on [a,b] and ∫ab= l f(x) l dx = zero then f(x) = 0 for all x in [a ,b]. Homework Equations Hint- from book- Section 2.4 Exercise 50 Let f and g be continuous at c. Prove that if: (a) f(c) > o, then there exists delta > o such...

Homework Statement Let p>0. What is the derivative of |x|^{p}? Homework Equations The Attempt at a SolutionI know that if p is even, then the derivative is just px^{p-1} . But what if x is odd? Would it turn out to be some piecewise function, such as px^{p-1},\: if x \geq 0 and -px^{p-1}...

Alright, I'm completely confused. I was given a study guide for my Algebra 2 exam(this isn't homework...) and one of the questions was 2|3x+5| < 16 I've seen the absolute value, but never seen a number in front of it...How do I solve this ?

I never really understood why using the Root Mean Square of negative data is the preferred method of finding the average of the data as opposed to taking the absolute value of the data and taking the average (arithmetic mean) of that. The example that recently made me wonder about this is...

Two rays of light of wavelength 650 nm and 420 nm are normally incident on a different grating. If the grating has 5000 slits/cm, what is the angular separation of of the two light rays' second order maximum. -Need to find the absolute value of theta 650-theta 420 I know I need to use...

Hey. I have | tn - t | < M How can i show that t - M < tn thanks

I have a problem in understanding the procedures of a solved example. It goes like this. \left ( \frac{z+i}{z-i} \right )^4 = -1 Therefor we can write: \left | \frac{z+i}{z-i} \right | = 1 From that we can see that z is a real number because: \left | z+i \right | = \left | z-i...

Hello there. I'm having some problems with absolute values when they contain multiple "abs" operators and some other numbers outside the "abs"-es. For example: \left | x+2 \right | - \left | x \right | > 1 If i check it for the positive scenario, the result is true for all x-es. x+2...

Are lx3l or lxl3 polynomials? If not, what would be a good example of a cubic polynomial function (R \rightarrow R) that doesn't cover all real numbers in its codomain?

Homework Statement prove |arctan(x)-arctan(y)| \leq |x-y| The Attempt at a Solution I tried separating cases: 1. both x and y are in the same quadrant; 2. x and y are not in the same quadrant; 3. x and y are zero (trivial); 4. either x or y is zero. Now, i can see why each of these is...

how do you go about solving abs value inequalities with double variables when the abs value bars are on both the variables? eg; |x| + or - |y| =, >, <, a

Homework Statement prove that llal-lbll\leqla-bl Homework Equations Triangle inequality lx+yl\leqlxl+lyl The Attempt at a Solution Let a=(a-b)+b By using the triangle inequality we get lal-lbl\leqla-bl Then from here I am not sure what I can do. I would like to say on the left...

Homework Statement Then find the area S of the region. (between the curves) Homework Equations A = \int_a^b f(x)-g(x) dxThe Attempt at a Solution First I plotted both equations, determined the top and the bottom functions and found where they intersected (calculator). Then I set up the...