1. ### B Is this true? The area of a circle can be approximated by a polygon

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...
2. ### Limit of the remainder of Taylor polynomial of composite functions

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...
3. ### I Is my interpretation of this three dimensional improper integral correct?

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...
4. ### I Does this limit exist?

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...
5. ### I Showing that a multivariable limit does not exist

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...
6. ### A limit problem without the use of a Taylor series expansion

I tried substituting x=cos2theta but it was of no use.I thought many ways but i could not make 0/0 form.So please help.
7. ### A trignometric limit going to infinity

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...
8. ### B Is there a condition for applying standard limits?

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...
9. ### How shall we show that this limit exists?

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}##...
10. ### I Why ignoring the contribution from point r=0 in eq (1) and (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...
11. ### B 1 to the power of infinity, why is it indeterminate?

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?
12. ### Limit of a root at infinity

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...
13. ### MCNPX - Question in SDEF card about AXS and EXT

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...
14. ### On the algebra of Limits

Homework Statement Find y; $$y=\lim_{x \rightarrow 0} {\frac {1} {x^2}-\frac{1}{tan^2(x)}}$$ Homework Equations $$\lim_{x \rightarrow 0} {\frac{tan(x)}x}=1$$ $$\lim_{x \rightarrow 0} {\frac{sin(x)}x}=1$$ The Attempt at a Solution \begin{align} y & = \lim_{x \rightarrow 0} {\frac {1}...
15. ### Limit of the form ∞-∞

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...
16. ### Limit of the form 0/0

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]
17. ### Multi variable Limit

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...
18. ### Proof of uniqueness of limits for a sequence of real numbers

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...
19. M

### Can somebody tell me what this topic is?

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.
20. ### I Differentials of order 2 or bigger that are equal to 0

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...
21. ### Evaluating limits

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?
22. ### I Is it possible to find the limit of (1+1/x)^x as x approaches -infinity?

Is it possible to find the limit of (1+1/x)^x as x approaches minus infinity using only the fact that it is e if x approaches infinity?
23. ### Lim x->0+ (x^cos(1/x))

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?
24. ### Convergence in distribution example

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...

30. ### I Question about Accumulation points

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...