Interval Definition and 677 Threads

Homework Statement [n=0 to ∞] ∑x2n/n! Homework Equations The ratio test The Attempt at a Solution So, here is the ratio of of the (n+1)th term to the nth term: | [x2(n+1)/(n+1)!] / [x2n/n!] | = | [x2nx2/(n+1)!] * [n!/x2n] | = | x2/n |, which will be will be less than one when n is big...

How would you go about finding the confidence interval for the parameters of the gamma distribution? I have had a look online and haven't found anything with the answer... Thanks

Homework Statement g(x)=ex and the x-axis on the interval [0,ln(9)] a) Set up definite integral that represents area b) Find area using fundamental theorem. Homework Equations The Attempt at a Solution g(x)=ex [0,ln(9)] \int^{ln(9)}_{0}e^x dx = [eln(9)]-[e0] = [9]-[1] = 8...

Homework Statement f(x)=cosx and the x-axis on the interval [0,2pi] A) Set up definite integral that represents area above B) Find area using the fundamental theorem Homework Equations The Attempt at a Solution cosxdx [0,2pi] = sinx [0,2pi] = sin(2pi)-sin(0) = 0 Area=...

Homework Statement Consider the initial value problem t*y' + 2y = e^(2t) ; y(1) = 0: Determine the largest interval on which it is guaranteed to have a unique solution. Homework Equations The Attempt at a Solution I just need somebody to tell me if i have a logic on this one...

Homework Statement First of all, in the below equation, it won't let me display it correctly. In the denominator is supposed to display 3^(n-1), NOT 3(n-1). So, I need to find the convergence interval and check the points. So far, I've found the intervals and checked both of the points to...

Homework Statement ln(3x+5) Determine intervals on which the function is increasing, decreasing, concave up, and concave down. Homework Equations The Attempt at a Solution So I did f '(x) = 3/3x+5 this gives me 3x+5 = 0, and I get x = -5/3 (point where the y is zero) Now, I...

I have been working through Schutz's A First Course in General Relativity and was a little confused by how he presents the space time interval: \Delta \overline{s}^2 = \sum_{\alpha = 0}^{3} \sum_{\beta = 0}^{3} M_{\alpha \beta} (\Delta x^{\alpha})(\Delta x^{\beta}) for some...

Homework Statement I calculated T_o to be 1.27 seconds and "T_o"' to be 1.23 seconds, each representing a normal mode of oscillation. These are correct according to the text. Here is the question: what is the time interval between successive maximum possible amplitudes of one pendulum after...

Homework Statement What formula do I need to find the confidence interval, when I have got: - Number of samples - Level of Confidence - The assumed (1st guess) accuracy Homework Equations I found the following equation online: µ = z * [p * (1 - p) / n] ^ (-1/2) The Attempt at...

Homework Statement f(x) = x^3 + 12x^2 - 27x + 11 Absolute Maximum Absolute Minimum on the interval [-10,0] (there are 3 different interval sets, but if I can do this one, I think I can figure out the rest.) Homework Equations Derivative, set equal to 0, then solve for the problem, but...

Homework Statement Consider two events ct_{1}\; =\; 3\; m,\; x_{1}\; =\; 2\; m,\; ct_{2}\; =\; 5\; m,\; x_{2}\; =\; 6m What is the time difference between the two events? Find a reference frame for which the time difference is the negative of the time difference in the original frame...

Hi, This might be a trivial question, but I'll ask it anyway. Why is this not an open interval? Let a, b be two elements in X, such that a < b. Then, every real number c satisfying the order relation a < c < b is necessarily in (a, b) and hence in X. Hence X is an interval. Since X is...

Given the fact that the following inequality must hold; x > y-1 For all y \in ]0,1[ (an open interval) and given the fact that one can choose y After one chooses x, can one then state that x > 0 holds? My idea was to say that at least x >= 0 holds because: 1) Someone picks a negative x...

Homework Statement on a spacetime plot (y-axis) = t (x-axis) = x find the spacetime interval between points (0,0) and (300,700) Homework Equations Interval = (c^2(del t)^2 - (del r)^2)^1/2 The Attempt at a Solution So I can see clearly my del t is 700 (700 - 0 = 700 ) but for the...

Can a function be continuous on a composed interval? For example, if f(x)=\frac{1}{x} then on the interval (-\infty,0) \cup (0,\infty), f(x) is continous? Or is the function f(x) continuous on (-\infty,0) by itself and (0,\infty) by itself (If you don't get what I'm trying to say reply back)?

Homework Statement Find the radius and interval of convergence of the power series: \sum_{n=1}^{\infty} \frac{x^{2n-1}}{(n+1)\sqrt{n}} Homework Equations .. The Attempt at a Solution My soltion: the ratio test will gives |x^2|=|x|^2 it converges if |x|^2 < 1 i.e. if |x|<1 i.e...

Hi, I need to find out what the largest interval in which the given intial value problem is certain to have a unique solution. I don't really know how to approach this problem though, I have a theorem on existence and uniquness of solutions but I'm finding it hard to make sense of it. I've got...

Homework Statement Hi all I wish to show differentiability of g(x)=x on the interval [-pi, pi]. This is what I have done: g'(a) = \mathop {\lim }\limits_{h \to 0} \frac{{g\left( {a + h} \right) - g\left( {a} \right)}}{h} \\ = \mathop {\lim }\limits_{h \to 0} \frac{h}{h} \\ = 1...

Homework Statement During a 4.95 s interval, a particle's coordinates change from x = 10.4 m, y = 4.95 m to x = 31.5 m, y = -4.95 m. Assuming the particle's velocity is constant, what will its coordinates be at the end of the next 4.95 s interval? x= ____m y= ____m Homework Equations The...

Homework Statement Nested interval theorem: Suppose [an,bn] is a nested sequence of closed intervals, i.e. [an+1,bn+1] is contained in [an,bn] for all n≥1. Then the intersection of all these intervals is nonempty. Proof: an is an increasing sequence bounded above by b1 (or any bn), so...

If we have a Lagrangian which looks like this: L=\frac{m}{2}g_{ij}(x)\dot{x}^i\dot{x}^j where: ds^2=g_{ij}(x)dx^idx^j If we are told that: ds^2=d\phi^2 +(sin^2 \phi) d\theta^2 How can we show that the Lagrangian is: L=\frac{m}{2}[\dot{\phi}^2 +(sin^2 \phi) \dot{\theta}^2] Is there a...

Solve Inequalities with answers in Interval notation. x^2 + 1 > 4x Solve for x, U = Union x^2 - 4x + 1 > 0 x= 3.732050808, 0.2679491924 Answer x= 3.732050808 U 0.2679491924 ?

Homework Statement Prove that in any interval there exists an irrational z. Homework Equations The Attempt at a Solution My professor wrote this for me when trying to explain how to prove this: a \notin Q, \epsilon rational [r, s]\in a l([r, s])<\frac{\epsilon}{2}...

Homework Statement Prove that in any interval there exists a rational z. Homework Equations The Attempt at a Solution My professor wrote this for me when trying to explain how to prove this: a \notin Q, \epsilon rational [r, s]\in a l([r, s])<\frac{\epsilon}{2}...

hey there.. i hope u guys can help me.. the question is... Determine the interval and radius of convergence of the power series below.. \sum\limits_{k=0}^\infty[SIZE="4"]k!(x-3)^k i've already find the radius, r = 0 then.. c - r < x < c + r 3 - 0 < x < 3 + 0 hence, x = 3 when x =...

hey there.. i've try this question(attachment) already... i got radius of convergence, R = 1/8 at x = 1/8, converges... at x = -1/8 i don't how to do this one.. please help me..

Hi, I'm studying for the final exam in my first course in topology. I'm currently recalling as many theorems as I can and trying to prove them without referring to a text or notes. I think I have a proof that the closed interval [0,1] is connected, but it's different than what I have in my...

Hi all, I am new to C and I need some help solving an issue with network programming. So in general, i have two programs running: Program A and Program B. Description of A: Send out packet with SN = i (SN is the label for the packet. i.e first pkt SN=1, 2nd pkt SN=2 etc) Set...

So we did a dry lab in class, and we were determining sources of error for a particular lab dealing with the measurement of rate of reaction. My teacher said that the time intervals of the recorded concentration was too far apart (1 minute intervals). I was wondering if anyone would explain...

Homework Statement Compute the area of the region S between the graph of f and g over the interval [0,2] if f(x) = x(x-2) and g(x) = x/2 Homework Equations The Attempt at a Solution The result is a(S) = \int_0^2 [g(x) - f(x)] dx = \int_0^2 (5x/2 - x^2) dx = 5/2...

The invariant interval is defined to be \Delta {s^2} = \Delta {x^2} + \Delta {y^2} + \Delta {z^2} - {c^2}\Delta {t^2} and despite which inertial frame we are in, \Delta s for two particular events would be the same. If I use Lorentz transformation, this can be proved easily. But is there any...

Suppose that a function f is differentiable at x0 and that f'(x0)>0. Prove that there exists an open interval containing x0 such that if x1 and x2 are any two points in this interval with x1 < x0 < x2 then f(x1) < f(x0) < f(x2). How do I establish an open interval? Do I need the "epsilon delta"...

By Weierstrass approximation theorem, it seems to be obvious that every continuous function has a power expansion on a closed interval, but I'm not 100% sure about this. Is this genuinely true or there're some counterexamples?

With one clock stationary at the common origin for 10 time units and the other rocket clock traveling out and back at v=.6c. When both clocks are compared at the origin the elapsed time on the traveling clock will show less time by a factor of (.8) from the Lorentz Transformation. The...

Hi, all, assuming a and b are random variables and their pdf f(a) and f(b) are known. then, how do I solve for the definite integral given as v=\int\limits_{a}^{b} g(x) dx, where g(x) is a function of x? or, how do I solve the pdf of v? Thanks a lot..

Calculus - please help find average rate of change of the function over a given interval Homework Statement h(t) = sin t, [3pi/4,4pi/3] please help me solve this, try to give me an explanation on every step please. i checked but i can't find anything on this in the book. i am...

Prove that if c and d are positive, then the equation \frac{c}{x-2} + \frac{d}{x-4} = 0 has at least one solution in the interval (2,4). I try to use the following theorem: If f is continuous on [a,b] and if f(a) and f(b) are nonzero and have opposite signs, then there is at least one...

Okay, tlet me know where I trip up: The everyday concept of "distance" allows an event to occur in only one place at one time and nowhere else. But because of the interval metric's signature (it has both positive and negative terms), the definition of four-dimensional distance implies that...

A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured(a display ad is a large block of multicolored illustrations, maps, and text). The data (in square...

Homework Statement Hey all. I'm being asked to find the radius and interval of convergence for the series from 1 to infinity: x^n/(1*3*5...(2n-1)) I have a feeling this is pretty straight forward (just apply the ratio test etc...), but my trouble lies in defining the denominator...

For an egg drop project, I have to calculate the time interval for which the force won't exceed 3 Newtons. The egg is dropped from a height of 12.19 meters, and the vehicle that carries it weights .454 kg. Calculating the force, I get .454kg*9.8 m/s^2m which equates to 4.44 Newtons. Is the 4.44...

Homework Statement Prove that I+J is the smallest interval containing all x+y, for x \in I and y \in J. Homework Equations I+J=[r+u,s+v]The Attempt at a Solution Let I=[r,s] and J=[u,v] Then I+J=[r+u,s+v] for all x \in I and y \in J x \in I means r \leq x \leq s y \in J means u \leq y\leq v...

Let S be an uncountable subset of the reals. Then does S always contain at least one interval (whether it be open/closed/half-open/rays/etc..)? Maybe the Cantor set is an example of an uncountable set that contains no intervals? How does one show this if it is true? My intuition is...

Latex Question: I am having a hell of a time finding how to put the large vertical bar used to denote the interval over which a definite integral should be evaluated. Can you please help me?

What does the term "complementary interval" mean? I'm studying the Cantor set and related notions right now, and I keep coming across the term "complementary interval." What does that mean? I can't find a definition spelled out anywhere!

Homework Statement I'm trying to find the arc length of a curve over an interval and I've arrived at \int (y4 +2y2 +1)1/2 dy and now I'm pretty sure i should use a u substitution in order to integrate. I tried using u=y2 so du=2y dy so dy=du/2y Then you have \int (u2+2u+1)1/2 and...

For any open interval containing limsup s_n, there exists infinitely many s_n... Hi all! I'm new to this fantastic forum! Please help me with the following problem! Thanks in advance! Homework Statement Suppose that the sequence (s_n) is bounded in \mathbb{R}. Prove: Given any open...

Find the arc length. x = sqrt(t) y = 6t - 2 Interval from 0 to 5 inclusive. Whenever I do this, I get a long answer with big numbers in the numerator all divided by 48. Can someone walk me through the steps? THanks.

Homework Statement (1 + 2*x exp(−y))dx − (1 + x^2) exp(−y)dy = 0 with y(0) = 0 Show that the equation is exact and hence find the solution of the initial value problem on the interval 0 ≤ x < 1. The Attempt at a Solution For the differential equation, after solving everything with...