Els Límits (Catalan pronunciation: [əlz ˈlimits]) is a Spanish village, a civil parish of the municipality of La Jonquera, situated in the province of Girona, Catalonia, in Spain. As of 2005 its population was of 115. Its Spanish name is Los Límites.
Homework Statement
Have a few limits that I'm stuck on:
a) lim n->infinity (n(n+1)^(n+1))/(n+2)^(n+2))
b) lim n->infinity (n^n/(n+3)^(n+1))
c) lim n->infinity n^(-1)^n
I've tried my best to understand what to do solve these, but can't get it. We've been given answers to standard...
Homework Statement
Use sandwich Rule to find the limit lim n> infinity (a_n) of the sequences, for which the nth term, a_n, is given.
Homework Equations
^{lim}_{n\rightarrow∞}\frac{n!}{n^{n}}
The Attempt at a Solution
I know by just looking at it, n^n Approaches infinity much...
Calculus 2: Sequence Limits Question to the power n??
Homework Statement
Find the limits (if it exists) to decide which sequences, whose nth term is given below.
Homework Equations
(\frac{3^{n}-4^{n}}{3n^{2}+4^{n}+7})
The Attempt at a Solution
I've done a few of these but as Soon as the...
When calculating the limit of the function f(x) = (x^2 + 3)/ sqrt(2x^4 + 5) as x→∞, is it correct to square the top and then place the resulting polynomial under a square root (i.e. sqrt(x^2 + 3)^2)? Then you can rewrite the problem as the square root of the limit as x→∞ of the resulting...
Homework Statement
X is uniformly distributed over [-1,1]. Compute the density function f(y) of Y = 2X2 + 1.
Homework Equations
The Attempt at a Solution
FY(Y) = P(Y < y) = P(2X2 + 1 < y) = P(X < +\sqrt{1/2(y-1)} = FX(+\sqrt{1/2(y-1)})
We have that f(x) = 0.5 for -1 < x <...
Here is the question:
Here is a link to the question:
Maths: Caluclus > Functions? - Yahoo! Answers
I have posted a link there to this topic so the OP can find my response.
I have the expression:
limb->-8[½b^2]-limb->8[½b^2]
Is it rigorously defined how to calculate this? The question arose because I want the additivity of improper integrals to work and if you take the integral of x from minus infinity to infinity to work the expression above must be zero.
Homework Statement
I need to find the volume of the region bounded by
(x-1)^2 + y^2 =1 \ \ \text{and} \ \ x^2+y^2+z^2=4 \ .
But I only need help setting up the limits of integration.
Homework Equations
The typical cylindrical change of variables.
The Attempt at a Solution
I have 0 \leq...
Hello,
I was studying the theorem of smoothness/compactness in Fourier theory and at the very last step of the proof one gets the result that \omega F(\omega)\to 0 when x\to \infty. The author of the book writes this result in little-o notation as: \omega F(\omega) = o(|\omega|^{-1}) which I...
I'm in analysis and I'm trying to understand the following.
Homework Statement
g(x) = integral from 0 to x+δ of f(x)dx + integral from x-δ to 0 of f(x)dx
g'(x) = f(x+δ) - f(x -δ)
So how do they get g'(x)?
Homework Statement
Let ##x_k=k## for ##k \leq 31## and ##\displaystyle x_{k+1}=\frac{x_1+x_2+...x_k}{k}## for ##k \geq 31##. Also let ##y_k=x_k## for ##k \leq 31## and ##\displaystyle y_{k+1}=\frac{y_k+y_{k-1}+...y_{k-30}}{31}## for ##k \geq 31##. Now if ##z_k=y_k-x_k## for all ##k ε N##. Find...
Homework Statement
Why is it that when using the comparison theorem my limits of integration must be from a constant value to infinity and not from negative infinity to infinity?
For example ∫ x/(1+x^2) dx from -∞ to ∞
Hi, all. I'm trying to ascertain whether it is remotely possible for a human being to survive acceleration from 100 to 7000 mph (essentially, from 0 to Mach 10) in say 5 seconds? 10 even? Assume the mass that of an ordinary man, and perhaps a co-pilot, the vehicle probably a prototype of modern...
I received permission from my father to post this from his (unpublished) Calculus text. Note that this method will, I believe, work for proving existence of a limit for a nonlinear function at any point that is not a local extremum. My father thought it would be good to give you this proviso...
Homework Statement
Prove that ##\lim_{x \rightarrow a} f(x) = \lim_{h \rightarrow 0} f(a+h)##.
Homework Equations
By definition, if ##\lim_{x \rightarrow a} f(x) = l## then for every ##\epsilon > 0## there exists some ##\delta_1## such that for all x, if ##0<|x-a|<\delta_1## then...
∞
∫ x/(x^2+1) dx
-∞
I basicaly evaluated the integral and Ln (x^2+1) as the antiderivative and when taking the limits I get ∞-∞
(ln |1| -ln|b+1|) + (ln|n+1|- ln|1|)
lim b-> neg. infinity lim n-> infinity
does this function converge or diverge? this was a question on...
Homework Statement
evaluate the integral 1/(u^2 -36) from 0 to 6
does the integral converge?
Homework Equations
The Attempt at a Solution
integral 1/(u^2 -36)
integral 1/((u-6)(u+6))
Partial fraction decomposition
1/((u-6)(u+6)) = A/(u-6) + B/(u+6)
1=A(u+6) + B(u-6)
1=(A+B)u +(6A-6B)
A+B=0...
So say I have an arbitrary function and I want to know it's limit as x,y approaches 0.
I could test what happens when the x-axis approaches 0, y-axis as it approaches 0 but there are some functions where I'm told that I also need to test what happens when y=mx approaches 0, and then y=x^2 and...
Hello guys, I am stuck in page 129 on Calculus Vol I - Apostol book. I would like to know if there is anybody here who can help me. I am not a mathematician, so It might be a simple transformation but I am not going through it.
He states that:
lim(x->p) f(x) = A is equivalent to say that...
I have the following integral:
\int_0^{f(x,y)}{f' \sin(y-f')df'}
Now suppose that f(x,y) = x*y, my question is how do I write the integral in terms of x and y only? Can I do something like this?
Since df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy we can obtain...
Homework Statement
a. lim
x→0
(x^3 − 2x + 7)/(3x^2 − 3)
b. lim
x→-1
1/(x+1)
Homework Equations
The Attempt at a Solution
For a. I obtained a limit of 7/-3
For b. the limit does not exist
(I really unsure about this)
Hi guys, I've been on quite a random change of variables binge lately and I've been messing around with a particular scenario in which I'm not 100% sure of how I should choose my limits of integration. Any help would be greatly appreciated! (And no, this is not homework, etc.) The scenario is as...
Homework Statement
∫e-Sxsin(ax) dx, S and A are constants, upper limit is ∞ lower is 0
Homework Equations
∫ u dv = uv - ∫ vdu
The Attempt at a Solution
After integrating by parts twice I got:
(S2)/S(S2+a2) lim c→∞ [-sin(ax)e-Sx + acos(ax)e-Sx] |^{C}_{0}
Okay, now how on Earth do I take...
I was fiddling around with the definition of limits at infinity and believe I have found a statement that is equivalent to the definition.
So the question is this: are the following two statements equivalent?
(1) \lim_{x\rightarrow\infty}f\left(x\right)=L
(2) \exists c>0\exists...
Homework Statement
The maximum deflection of a beam is given by the equation
y=M/P(sec(μL/2)-1)
μ=√(P/EI) Where EI Is a constant.
Show that as P→0 y→ML^2/8EI
This is a mathCAD problem by the way, but I'm very novice at it so i want to try formulise some sort of solution on paper...
Homework Statement
This is not really a homework or a coursework question. But I got a warning that I should submit my post in this section of the website.. I'm just saying this because I don't know if the answer to my question is at all achievable. And if it is how I should go about trying to...
Could someone look over this and see if I have any mistakes? I'm trying to show that
∫ y' dx = ∫ dy through definitions.
http://imgur.com/6zCHYo5
Thanks!
I want to show that if f(x) > g(x) \forall x \in (-\infty, \infty) and \displaystyle\lim_{x\to\infty}g(x)=\infty , then \displaystyle \lim_{x\to\infty}f(x)=\infty . This result is true, correct? If so, what theorem should I use or reference to show this result? I wasn't sure if...
I have a few questions for my homework assignments for solving limits, but in order to do those questions I have to use a few standard limits that we haven't been taught, which means I'll have to prove them. I know these can be done using L'Hopital's rule, but we haven't covered that yet so I...
(Hey guys and gals!)
Homework Statement
Given a bounded set x_n and for any y_n the following condition holds:
\limsup_{n \rightarrow ∞}(x_n+y_n) = \limsup(x_n)+\limsup(y_n)
Show that x_n converges.
Homework Equations
Definition of limsup(x_n) = L:
\forall \epsilon > 0 \mid...
I'm trying to find the integration of my function f[x] from 1 to 4 using the indefinite integral and inserting limits using rules. I am not sure how to insert the limits with rules, have been playing about with the following
Integrate[f[x], x] /. x -> {1 >= x <= 4}
which ain't working,
any...
Homework Statement
Evaluate the limit of each indeterminate quotient:
lim (x-->4) [2-(x^1/2)]/[3-(2x+1)^1/2]
Homework Equations
The Attempt at a Solution
The answer in the book is 3/4. This MAY be wrong though.
My attempt: I basically tried rationalizing the numerator AND denominator but...
Homework Statement
we have this function
f(x)=1 if \frac{1}{x}\in Z ( aka integer)
f(x) = 0 otherwise
Prove that limit (as x approach 0) dosen't exist (use the definition of limit - trying to prove that limit as x approchaes 0 and x approchs 0+ will not work here)<-- hint given by the...
lim e^(1/(6-x))
x->6+
Was wondering how to solve for this limit analytically. I plotted it and see it going to 0, but that is not the answer in the book.
A panel put out over 30.7 volts, say 34 volts and I have a micro-inverter that require a voltage of 11-30 to work. Other than shading some of the panel, is there a way to half the voltage from the panel without as much loss from shading some of the cells to work the inverter?
Homework Statement
lim x->4 (1/((sqrt x)-2))-4/(x-4)
Homework Equations
The Attempt at a Solution I have made several stabs at this problem. First I tried using values very close to 4 (e.g. sqrt of 4.001) Then I tried rationalizing the expression 1/((sqrt x) -2). That did...
(Hello everyone!)
Homework Statement
Given that \limsup_{n \rightarrow \infty}(\frac{1}{x_n})\cdot \limsup_{n \rightarrow \infty}(x_n)=1
Show that x_n converges.
Homework Equations
Recalling that:
x_n \text{ converges } \iff \liminf(x_n)=\limsup(x_n)
The Attempt at a Solution
Started with...
Homework Statement
Just checking if these are right?
f(b) = 2-2√b
compute limit in are as:
b-> 0+
b->1-
Explain in a brief sentence why it does not make sense to compute a limit as b->0-
Homework Equations
given above
The Attempt at a Solution
lim b->0+ (2-2√b) = 2...
I'm familiarized with finding limits of most kinds of functions. I was struck by a problem: What if the variables of the function belong to different sets of numbers?
My point being, given the function:
f(n,q)=\frac{n}{q}
With n belonging to the set of natural numbers and q belonging to the...
Homework Statement
I was trying to prove something and I ended up in a situation similar to,
(limit t\rightarrow0)(limit s\rightarrow0) f(x+s,y+t)
=(limit s\rightarrow0)(limit t\rightarrow0)f(x+s,y+t)
My question is when does this equality hold. I can't find it anywhere...
Homework Statement
Suppose the functions f and g have the following property: for all ε > 0 and all x,
If 0 < \left| x-2 \right| < \sin^{2} \left( \frac{\varepsilon^{2}}{9} \right) + \varepsilon, then \left| f(x) - 2 \right| < \varepsilon.
If 0 < \left| x - 2 \right| < \varepsilon^{2}...
Could someone explain what things like \displaystyle \lim_{x \to 3^+}\frac{1}{x} and \displaystyle \lim_{x \to 3^-}\frac{1}{x} are supposed to be?
I googled and it gave me epsilon delta stuff. I'm not smart enough for that. (Doh)
I guess I'm asking if anyone could give a dumbed down...
Homework Statement
Using the delta-epsilon definition of limits, prove that of lim f(x) = l and lim f(x) =m, then l=mHomework Equations
Delta-epsilon definiition of the limit of f(x), as x approaches a:
For all e>0, there is a d s.t if for all x, |x-a|<d, then |f(x) -l|<e
The Attempt at a...
Homework Statement
What would be the limits for each of the integrals (one with respect to x, one with respect to y) of an area bounded by y=0, y=x and x^2+y^2=1?
Homework Equations
None that I can fathom
The Attempt at a Solution
I've rearranged the latter most equation to get...
kevlar has the greatest tensile strength(yield strength here) in all materials at 3620 MPa , am i correct?
and i want to know which material has the least tensile strength(yield strngth)..