Hello everyone!
I have been looking for a general equation for any regular polygon and I have arrived at this equation:
$$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$
Where x is the side length and n the number of sides.
So I thought to myself "if the number of sides is increased as to almost look...
Since $$\lim_{x \rightarrow 0} \frac {R_{n,0,f}(x)} {x^n}=0,$$ ##P_{n,0,g}(x)## contains only terms of degree ##\geq 1## and ##R_{n,0,g}## approaches ##0## as quickly as ##x^n##, I can most likely prove this using ##\epsilon - \delta## arguments, but that seems overly complicated. I also can't...
In Physics/Electrostatics textbook, I am in a situation where we have to find the electric field at a point inside the volume charge distribution. In Cartesian coordinates, we can't do it the usual way because of the integrand singularity. So we use the three dimensional improper integral...
This question consists of two parts: preliminary and the main question. Reading only the main question may be enough to get my point, but if you want details please have a look at the preliminary.
PRELIMINARY:
Let potential due to a small volume ##\delta## at a point ##(1,2,3)## inside it be...
I want to show that the limit of the following exists or does not exist:
When going along the path x=0 the limit will tend to 0 thus if the limit exists it will be approaching the value 0
when going along the path y=0, we get an equation with divisibility by zero. Since this is not possible...
I wrote cos(pi(n^2+n)^(1/2)) as cot(pi(n^2+n)^(1/2))/cosec(pi(n^2+n)^(1/2)) and as we know cot(npi)=infinity and cosec(npi)=infinity , so i applied L'Hospital.After i differentiated i again got the same form but this time cosec/cot which is again infinity/infinity.But if i differentiate it i...
I came across this basic limits question
Ltx->0[(ln(1+X)-sin(X)+X2/2]/[Xtan(X)Sin(X)]
The part before '/'(the one separated by ][ is numerator and the one after that is denominator
The problem is if I substitute standard limits :
(Ltx->0tan(X)/x=1
Ltx->0sin(X)/X=1
Ltx->0ln(1+X)/X=1)
The...
Let:
##\displaystyle f=\int_{V'} \dfrac{x-x'}{|\mathbf{r}-\mathbf{r'}|^3}\ dV'##
where ##V'## is a finite volume in space
##\mathbf{r}=(x,y,z)## are coordinates of all space
##\mathbf{r'}=(x',y',z')## are coordinates of ##V'##
##|\mathbf{r}-\mathbf{r'}|=[(x-x')^2+(y-y')^2+(z-z')^2]^{1/2}##...
The potential of a dipole distribution at a point ##P## is:
##\psi=-k \int_{V'}
\dfrac{\vec{\nabla'}.\vec{M'}}{r}dV'
+k \oint_{S'}\dfrac{\vec{M'}.\hat{n}}{r}dS'##
If ##P\in V'##, the integrand is discontinuous (infinite) at the point ##r=0##. So we need to use improper integrals by removing...
I've been taught that $$1^\infty$$ is undetermined case. Why is it so? Isn't $$1*1*1...=1$$ whatever times you would multiply it? So if you take a limit, say $$\lim_{n\to\infty} 1^n$$, doesn't it converge to 1? So why would the limit not exist?
Homework Statement
Hi everyone, I'm currently making my way through Spivak's calculus and got stuck in question 41 of chapter 5. It's important to note that at this point, the book has only reached the subject of limits (haven't reached continuous functions, derivatives, integrals, series...
My code version is 2.7
I have a disk source of R=0.3 cm, 60 cm above in z axis. I want set limits for the x and y axis, but, I can only put one command "axs" and "ext". How can i define two limits with one command?
my code it is like this
SDEF pos=0 0 60 rad=d1 axs=1 0 0 ext=d2 PAR=2 ERG=0.018...
Homework Statement lim x~∞ 〈√(x⁴+ax³+3x²+ bx+ 2) - √(x⁴+ 2x³- cx²+ 3x- d) 〉=4 then find a, b, c and d[/B]
Homework Equations
all the methods to find limits
The Attempt at a Solution
it can be said that the limit is of the form ∞-∞.I am completely stuck at this question.the answer is a=2...
Homework Statement lim x~a 〈√(a⁺2x) -√(3x)〉 ÷ 〈√(3a+x) - 2√x〉[/B]
Homework Equations rationalisation and factorisation[/B]
The Attempt at a Solution i had done rationalisation but the form is not simplifying.plzz help me.[/B]
Homework Statement
https://gyazo.com/268bef206850bfbf30fb0cca3f783599 <----- The question
Homework Equations
The Attempt at a Solution
Had this on a test today, honestly not sure how to evaluate. I know you can pass the limit to the inside of arctan but I can't see how the inside goes to...
Homework Statement
[/B]
The proposition that I intend to prove is the following. (From Terence Tao "Analysis I" 3rd ed., Proposition 6.1.7, p. 128).
##Proposition##. Let ##(a_n)^\infty_{n=m}## be a real sequence starting at some integer index m, and let ##l\neq l'## be two distinct real...
Homework Statement
Could somebody link me to a youtube video explaining this topic, its from an exam paper at me college and I cant find notes on it.It think it has something to do with limits. Many thanks.
So I've seen in several lectures and explanations the idea that when you have an equation containing a relation between certain expressions ##x## and ##y##, if the expression ##x## approaches 0 (and ##y## is scaled down accordingly) then any power of that expression bigger than 2 (##x^n## where...
Homework Statement
Evaluate the following limit or explain why it does not exist:
limx→∞ 24x+1 + 52x+1 / 25x + (1/8)6x
The Attempt at a Solution
I know there is the method where you divide through by the highest term in the denominator, but can that be applied here?
Homework Statement
Homework Equations
The Attempt at a Solution
let y = lim x->0+ x^cos(1/x)
lny = cos(1/x)*lnx = (x*cos(1/x)) * (lnx/x)
x*cos(1/x) = 0 (sandwich theorem)
lnx/x = 0 (l'hopital)
so lny = 0
and y = 1
Is this correct?
Homework Statement
Homework Equations
[/B]
Definition: A sequence X_1,X_2,\dots of real-valued random variables is said to converge in distribution to a random variable X if \lim_{n\rightarrow \infty}F_{n}(x)=F(x) for all x\in\mathbb{R} at which F is continuous. Here F_n, F are the...
The definite integral of a function ##f(x)## from ##a## to ##b## as the limit of a sum is:
$$\int_a^bf(x)dx=\lim_{h\rightarrow 0}h(f(a)+f(a+h)+.. ..+f(a+(n-2)h)+f(a+(n-1)h))$$
where ##h=\frac{b-a}{n}##. So, replacing ##h## with ##\frac{b-a}{n}## gives:
$$\lim_{n\rightarrow...
Sorry, I mistakenly reported my own post last time. But later I realized that these limits do work. So, I'm posting this again.
I'm using these limits to check second-order differentiability:
$$\lim_{h\rightarrow 0}\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}$$
And,
$$\lim_{h\rightarrow...
I understand the conditions for the existence of the inverse Laplace transforms are
$$\lim_{s\to\infty}F(s) = 0$$
and
$$
\lim_{s\to\infty}(sF(s))<\infty.
$$
I am interested in finding the inverse Laplace transform of a piecewise defined function defined, such as
$$F(s) =\begin{cases} 1-s...
This is mostly a procedural question regarding how to evaluate a Bromwich integral in a case that should be simple.
I'm looking at determining the inverse Laplace transform of a simple exponential F(s)=exp(-as), a>0. It is known that in this case f(t) = delta(t-a). Using the Bromwich formula...
I can't prove it and I've got it by some intuition because not many properties of superlogarithms are known. I don't think anyone can prove it but is there some way to at least check if it is correct.
The limit is:
$$\lim_{h\rightarrow0}slog_{[log_xx+h]}[log_{f(x)}f(x+h)]$$
where ##slog## is the...
So we just recently did accumulation points in my maths class for chemists. I understood everything that was taught but ever since I was trying to find a reasonable explanation if the sequence an = (-1)n has 2 accumulation points (-1,1) or if it doesnt have any at all. I mean it's clear that its...