Limits Definition and 1000 Threads

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...

Homework Statement 1. sin(1/x) as x->infinity 2. tan(7x)/sin(5x) as x->0 3. General question--when finding the derivative (through implicit diff.), and I have something like y=(5x^2)y, what parts am I supposed to use the chain rule, and when am I supposed to use the product rule? The...

Small question concerning limits' definition Hello, Every time I encounter the formal definition of a limit, namely : "For every ε>0 there is some δ>0 such that, for all x, if 0 < |x - a| < δ, then |f(x) - l| < ε" I always wonder why we need to write the left bound ( 0 < ) for the |x...

Homework Statement I am having trouble understanding when limits are undefined and when they do not exist. I googled it and cannot find a good explanation. Can someone please explain this to me? Homework Equations The Attempt at a Solution

Homework Statement \lim_{x→1}(frac(x)+frac(-x)) frac() is the fractional part function. Homework Equations The Attempt at a Solution I tried it by graphing. Firstly i drew the graph of frac(x) and then frac(-x). I added them. The resulting graph was constant at 1 but...

This is very basic. I have asked some friends and they don't know. I have tried resolving it by long division, and can see where the 1 comes from but the remainder is 1. I have gone back to the basics, but the operands are multicative. ie 1/a * a = 1 What is the algebra of this The problem...

Homework Statement Limit a\underline{}n as n→∞ = a. Find the limit a, and Determine N so that absolute value(a\underline{}n - a) < \epsilon for all n>N for the given value of \epsilon. The problem that I am working on is: a\underline{}n = 1/n , \epsilon = 0.01 I'm sure this is very...

Homework Statement Let a>1. Prove the limit as n goes to \infty of a1/n = 1. The Attempt at a Solution Given \epsilon > 0, \foralln>N, |a1/n-L|<\epsilon and N=(a-1)/\epsilon. |a1/n-L| = a1/n-1 ...and that's where I get confused. I know that I have to multiply (a1/n-1) by something...

Hi to all of Physics forums community :), I'm not sure whether or not I am in the right section. If not, I apologize for my mistake. Also, I am new to Calculus (I am in Cegep --> Quebec schooling system...) and I am taking Calculus 1 single variable. My teacher just started our class by...

Does anyone know what the limit is for light from distant objects to be so redshifted that they become undetectable? Could there be a way in detecting objects beyond this barrier? Would any wavelength at all be detectable?

Homework Statement So, the question is about evaluating limit of the equations given. The right and left hand sides should be found so that we can see if the limit exists or not. I am not sure how to write this in, but basically they're like both put in a big "{" so, i'll write both with an...

Homework Statement Use The Formal definition of limits to show Homework Equations The Formal definition of limits The Attempt at a Solution Tried to do it like this, but that was wrong. What do i need to do different?

Homework Statement a) Determine the points where the function f (x) = (x + 3) / (x^2 − 3x − 10) is discontinuous. Then define a new function g that is a a continuous extension of f . b) Determine what value of the constant k makes the Piecewise function { (x − k)/ (k^2 + 1) ...

Homework Statement I'm confused about a certain aspect of shell method, washer method, and disk method. If I want to rotate using the washer method about the x-axis how do I get the new limits of integration? For example: y = 9-x2 over [0,3] about x-axis. I solved for x and got: x =...

Homework Statement Say you have a nonconducting spherical shell. A is the inner radius and B is the outer radius. If you wanted to set up an integral to find the flux, would the gaussian surface include B, or be just inside it? That is, would the limits of integration go from A to B? If...

Homework Statement Postal charges are $.25 for the first ounce and $.20 for each additional ounce or fraction thereof. Let c be the cost function for mailing a letter weighing w ounces. a) Is c a continuous function? What is the domain? b) What is c(1.9)? c(2.01)? c(2.89)? c) Graph the function...

Homework Statement find the positive integers k for which lim x->0 sin(sin(x))/x^kHomework Equations exists, and then find the value of the limit The Attempt at a Solution I did the first three k's k=0 lim x->0 sin(sin x))/x^0= 0 undefined k=1 lim x->0 sin(sinx))/x^1= 1 k=2 I might be...

We have to graph these functions where they are real. (no need to graph where complex) d) For d I am getting a point at (1,0) and then half a c shaped graph opening towards the right. Is this correct? g) For g I have 0 on the negative side. and a straight line in the first quadrant. :s...

Hello, I'm currently trying to get my Ti-89 Titanium to compute the following triple integral; f(x,y,z) = xy(1-z) where 0<x<1, 0<y<1, 0<z<1, and x+y+z<1 int(int(int(f(x,y,z),x,0,1-y-z),y,0,1-z),x,0,1) The problem is that I can't get my Ti89 to substitute in for the limits of...

How to set "vector limits" when doing an integration in Matlab? I come across a trouble when I tried to set the limits of the integration as vector: %__________________________________________% b=1:3; c= quadv(@(x) x.^2+b, b, b+20); %__________________________________________% Then Matlab...

first of all i don't know anything about this epsilon and delta method.explain this a bit. secondly i have been given a problem involving this method: f(x)=x^2 given: limit x-->2 [x^2] = 4 a) what is the value of x' such that f(x')= 4 + .01? find \delta=x'-2 b) what is the value of...

Homework Statement Find the following limits, if they exist: h) lim absolute value[x]/(x) x->0^{+} and i) lim absolute value[x]/(x) x->0^{-} Homework Equations Not sure The Attempt at a Solution The answer to h) [according to...

Homework Statement Suppose |f(x)-5|<0.1 when 0<x<5. Find all values \delta>0 such that |f(x)-5|<0.1 whenever 0<|x-2|<\delta Homework Equations The Attempt at a Solution I know that 0<|x-2|<\delta 2-\delta<x<2+\delta \delta=2 but how does this part of the equation help me find...

Homework Statement Evaluate lim ((2+h)^4 - 16)/h h->0 Homework Equations Difference of squares The Attempt at a Solution knowing that the top of the fraction is a difference of squares i factored it and arrived at lim h->0 ((2+h)^2+4)((2+h)^2-4)/h this is where i got stuck

Hello! I am confused as always, but this time about the following: In a physics textbook, the following happens: From Newtons second law, V is the velocity and is a function of time, t is time, i is initial and f is final. \begin{equation} m\frac{d}{dt}(v) = F(t) \end{equation}...

Homework Statement Consider the linear differential equation εx'' + x' + x = 0, subject to the initial conditions x(0) = 1, x'(0) = 0. a) Solve the problem analytically for all ε > 0. b) Now suppose ε≪1. Show that there are two widely separated time scales in the problem, and estimate...

Homework Statement May seem easy to people but I have no idea how to do this :frown: lim_{x\rightarrow0}\frac{sin x}{2x^{2}-x} Homework Equations The Attempt at a Solution I factored out an x from the bottom but that really makes me see nothing else to do.. So I tried the quotient...

okay so I just have a question about using substitution when solving limits. Say I have the function sinx/x, if i want to find the limit when x--> 0 using approximation ( i know how to prove it with the pinching theorem by the way). So if I substitute 0.0000000001 rad into the function i get...

Just started learning limits today but I got stuck on this last problem... Let f be the function given by f(x)=lnx/x for all x>0 Find lim f(x) as x-->0+ So I graphed the equation and plugged in points approaching zero on the right side but it seems to go on for infinity. Is the limit...

Why is it that lim n->inf sin(n)^(1/n) = 1? I can't seem to figure it out why, thanks for any help that you can provide.

Homework Statement The question asks me to find the coordinates of the centroid of a uniform lamina enclosed by curve y=1-x^2. X axis and Y axis are in the 1st quadrant. Can you please tell me how to work out the limit for this equation?

Homework Statement i have the region given as being bounded by x2+y2=4 and z=0 and z=3. this problem asks to prove gauss divergence theorem for a given vector F Homework Equations The Attempt at a Solution As for the volume integral, i had no problem. But for the surface integral, how...

Have a couple of questions that I've been stuck with for some time. Would greatly appreciate the help. No idea how I should approach these questions and how do I start. 6. Suppose that a function f is continuous on the closed interval [0,1]and that 0≤f(x)≤1 for every x in [0,1].Show that...

Homework Statement http://i.imgur.com/F6qLL.jpg In the example, it says if the approaching path of the limit is y=x^2 and x=y^2, the limits are 0. I can see the limit is 0 for approaching in the path of x=y^2 since the function becomes f(x,y) becomes f(y^2,y)=3y^5/(y^4+y^2) \rightarrow 0 as...

Is there a real-valued function which is discontinuous everywhere, but which has a limit at every point in it's domain? My intuition is that this couldn't occur because, if the limit exists at some x, then it must become "increasingly continuous" in the vicinity of x (otherwise we could find...

Homework Statement The first problem I'm having difficulty with is \stackrel{lim}{x\rightarrow0} \frac{sin x}{5x} And the second is: \stackrel{lim}{x\rightarrow0} \frac{sin x(1-cos x)}{2x^{2}} Homework Equations I assume that for the first problem I need to simplify it to the rule...

In at least one book and one Wikipedia article, I've seen someone specify which sequences are to be considered convergent, and what their limits are, and then claim that this specification defines a topology. I'm assuming that this is a standard way to define a topology. I want to make sure that...

if say the function f(t) is 0 from 1 to 2 is 1 from 2 to 3 if i laplace transform it , for f(t) = 1, i get f(s) = 1/s so what are the limits for my s ? is it still 2 to 3? thanks!

I'm confused as to when to change the limits on a definite integral. Ex. Integral with the limits a=1, b=5, 3/(x+1)dx I set u = x+1 and du = dx I used u-substitution and everything worked out fine. However for this one... Ex. Integral with the limits a = 0, b = 2...

Homework Statement I'm doing an assignment, and I've hit a wall with this limits question: 6. If the limit as x approaches 0 of http://www2.wolframalpha.com/Calculate/MSP/MSP202919ggbg4de783c0e7000024ba5hah2cdg59e6?MSPStoreType=image/gif&s=14&w=106&h=41 equals \sqrt{5}, deduce...

Homework Statement We are required to sketch a (reasonably accurate) picture of a rational function f(x) = P(x)/Q(x) with P, Q polynomials in x and Q nonzero. We know that the roots of Q(x) are, say, x1, x2, etc. and so f(x) is (typically) asymptotic to the vertical lines x = xk for each k...

Limits- need help! Hi all, I am currently doing calculus in maths and finding it difficult, keep going through the material but its not making sense and not providing much explanation on solved problems. Can anybody help me with a few questions, i have attempted them but would...

Homework Statement So I'm trying to evaluate the following integral: 4\pi r^2{\int_0}^\infty r^2\frac{\sin{sr}}{sr}dr which after canceling out one of the r's, gives an integral similar to that of xsinx. I need to show that this integral vanishes for all values of s that are not 0...

Homework Statement Evaluate f(x,y)=y2\sqrt{1-x2} over the region x2+y2< 1 Homework Equations The Attempt at a Solution using x limits between -1 & 1 followed by the y limits of 0 & \sqrt{1-x2} \int\inty2\sqrt{1-x2}.dy.dx Evaluating this and multiplying be 2 to get the...

Homework Statement limx->\pi/2(ln sin x)/((\pi-2x)2)Homework Equations The Attempt at a Solution Putting \pi/2 into this equation gives 0/0, however, the limit of this could be 1,0 or infinity, so how would you distinguish between the three?

question is limx->0 (1+x+x^2-e^x)/x^2 How i did it. =>limx->0 (1-e^x)/x^2+(x+x^2)/x^2 =>limx->0 ((1-e^x)/x)*1/x+1/x+1 using limx->0(e^x-1)/x=1 =>limx->0 (-1)*1/x+1/x+1 =>limx->0 1 =>Answer=1. (hope you understand my writing way. Where are list of tags for this forum) I think i do nothing...

Question: Suppose that f(x)>0 on (0,1) and that lim as x goes to 0 exists for the function. Show that lim as x goes to 0 for the function is greater than or equal to 0. So I know that intuitively that this is true for obvious reasons, but I can not think of a clever way to set up the proof...

I've built a model rocket with the longest burning engine I could find, a light sensor in the nose cone, accelerometers on the forward fins all connected to an Arduino pro mini microcontroller programmed to keep it pointed at the brightest source of light. If I attach this rocket to a balloon...

Consider this very simple example of limits limitx->2 (x2-4)/x-2 value of function at x=2 is not defined. but rearranging function like this limitx->2 x+2 gives us it's limit at x=2. My question is how rearranging a function gives limit of that function at the specified point.. I have...

Why wouldn't answer choice "C" be true as well? [PLAIN]http://i.min.us/idPNiK.png Homework Equations I thought that you could use direct substitution on this limit. The Attempt at a Solution I did get answer choices A and B. For the limit to exist, both the left and right hand limits...