Absolute values Definition and 77 Threads

sin|x + y| = ? cos|x + y| = ? Is there any formula for these?

In a lot of compilations of standard integrals (my Calculus book does this, Wikipedia does this), a lot of the integrals of trigonometric functions have an absolute value in their solution which seems out of place to me. For example, take the integral \int dx \cot{x}. My Calculus book says...

Hi! I've got a problem that's got me a bit.. well, in the end I guess the proper word is sceptic, because it feels a bit like I've made the answer up, which is why I'm taking it up here at all. Anyway: Homework Statement Determine the domain for f(x) and the asymptotes to the curve y=f(x) for...

Homework Statement So I've got two problems I'm struggling a bit with. One of them I've solved (I think), but I'm definitely not sure. The other one is bugging me a bit. Anyway: i] Determine all z∈C so that |z - 1| = 5 and |z - 4| = 4 ii] Determine all z∈C so that |4 - z2| = z...

Homework Statement http://img3.imageshack.us/i/0902091724.jpg/ http://img3.imageshack.us/i/0902091724.jpg/Homework Equations The Attempt at a Solution My problem is that I don't even know where to start on this! My first problem is always forgetting what I can and can't use, because we can...

Homework Statement Evaluate. lim |x+1| x-> -1 Homework Equations The Attempt at a Solution Not too sure what |x+1| means. I think it has something to do with an absolute value... would the answer be 2 then?

Homework Statement I do not see how the two equations in each example are related, what should I do with them? (the l's are absolute value brackets): a) Let g(x) = 3x - 3 + l x+5 l. Find all values of a which satisfy the equation: g(a) = 2a +8 b) Let h(x) = l x l - 3x...

Hi all, I'm currently preparing for pre-tertiary mathematics, studying from Apostol's "One-Variable Calculus". I have just begun to work on the theory of integration of trigonometric functions, but I found that with the last set of exercises (on finding area between two functions, over some...

Homework Statement Find the Local and absolute extrema of f(x) on the interval [-1,2] and give a sketch of the graph if: f(x) = [ 1 / (1 + |x|) ] + [ 1 / (1 + |x - 1|) ] I am confused about the absolute value parts. I know they're the versions inside the absolute value signs when...

Homework Statement I reduced a much harder problem to the following: Prove that if abs(a-b) is divisible by k, and if abs(b-c) is divisible by k, then abs(a-c) is divisible by k. Homework Equations none really. The Attempt at a Solution I tried setting abs(a-b)/k = n and abs(b-c)/k = m...

Homework Statement lxl <2 lx+2l The question is asking to solve this Homework Equations The Attempt at a Solution Ive tried bringint the 2 over which leads me to l-x-4l over lx +2l < 0 but then the absolute value confuses the heck out of me on where to go...

Homework Statement \int|x^{2}+x-2|dx from -2 to 2 Homework Equations The integral of f(x) from a to b = F(b) - F(a) |x| = { x if x >= 0; -x if x < 0 --- Ok, I don't know how to do the definite integrals of absolute values.. was never shown an example of it in class, but I kind of...

Homework Statement Where is the function f(x) = |x| differentiable? Homework Equations [f(x+h) - f(x)] / h The Attempt at a Solution I know that the graph of f(x)=|x| shows a corner at the origin from which 2 lines project at opposite slopes, as in they are symmetric about the...

Homework Statement We recently proved that if a function, f, is continuous, it's absolute value |f| is also continuous. I know, intuitively, that the reverse is not true, but I'm unable to come up with an example showing that, |f| is continuous, b f is not. Any examples or suggestions would...

Homework Statement \int_0 ^\pi \sqrt{1-\sin^2 x} dx Homework Equations 1 - \sin^2 x = \cos^2 x The Attempt at a Solution I don't know how to treat this since cos changes sign half way across the integral. I know the answer should be 2 but I keep getting 0 every which way I try.

I need help finding limits. I know it's pretty simple most of the time... I know that for example if the lim x--> 3 of x-3, you just plug 3 for x... what do I do if it's the absolute value of x-3? I know you guys like to see that I've tried to solve the problem, but there's not much I can...

Hello again. I have a (stupid, but I'm not real sure about the answer-type) question. I'm trying to prove that the second order ODE of the simple pendulum y''=-(g/l)sin y is Lipschitz (using norm 1). After doing some evaluating, I came up with |u'-v'| + |\frac{g}{l}||\sin u - \sin v| All I'm...

Hi, I'm stuck on the following problem: |(4/x)| > 5 I split it up into two cases, case 1 is x > 0, case 2 is x < 0 Case 1: Case 2: 4/x > 5 4/x < -5 4 > 5x 4 < -5x 5x < 4 -5x > 4 x < 4/5...

I need a little help and reassurance here. The question is as follows, Find the following limit, if it exists. \lim_{x \rightarrow 1} \frac{x ^ 2 + |x -1| - 1}{|x-1|} Here is what I did, first I did the two one-sided limits, as \lim_{x \rightarrow 1^+} and as \lim_{x \rightarrow 1^-}. (the...

An example in my textbook gives \vert \frac{5-x}{5x} \vert \Leftrightarrow \frac {1}{5} (\frac{1}{\vert x \vert}) (\vert x-5 \vert) Is there something I don't know about absolute values that allows \vert 5-x \vert to become \vert x-5 \vert or is this a mistake in the text?

so if |x|=(x,if x>=0, and -x, if x<0) then what would be like |x-7| be equal too and how do you do this i do not understand why |x|equals (x,if x>=0, and -x, if x<0) could you explain it to me?

I'm supposed to sketch this graph \vert x \vert + \vert y \vert = 1 + \vert xy \vert I think the purpose of the exercise is to simplify this into something that resembles a typical function and be able to shift the graph over so that it looks normal. I'm having troulbe getting the y's...

This is easy, but for some reason I can't grasp the idea. |x-1|+|x-2|>1 I know it means that the distance between x and 2, and x and 1 is larger than 1. It isn't school related, and I did search online, but they are simple ones like... |x-1|>1 Can anyone help me? Thanks.

Can someone give me a n00b lesson in absolute values, i though i remembered, but i don't. I got stuck on a -|-8| :blushing:

I have to solve the integral: \int^1_{-1} e^{-| |x| - \frac{1}{4} |} dx but I have no idea what to do with the absolute value signs. Can someone help me? :confused:

1) │3x-2│<= x+1 ; x>=-1 Case1: 3x-2>=0 x>= 2/3 3x-2<=x+1 x<=3/2 what is case 2? 2) │2-3x│ < 3x-4 3) │x-3│=x-2 How do u solve these?

Does anyone know how to put absolute values in the t1-83 graphing calculator? I need to graph absolute value of x, the absolute value of x +2, and the absolute value of x-3