Limits Definition and 1000 Threads

The "importance" of Limits Hey, I am a student in the physics and engineering fields. I have been doing calculus for two years. I understand that the limit is, in a sense, the "building block" of calculus. Differentiation and the derivative is defined by calculating the difference quotient...

I've been doing some chemistry, and come up with a confusing problem that I can't seem to solve. It's a problem I made up while trying to understand the Gibbs Free Energy, but I will try to phrase it solely as a calculus question. It is known that \Delta G + \epsilon \Delta S < 0 and that...

Homework Statement Show that lim (x,y) → (a,0) e^(x ln y) = 0 \foralla > 0 Homework Equations The Attempt at a Solution I've tried looking at lim (x,y) → (a,0) x ln y seperately. lim(x,y) → (a,0) x ln y = lim(x,y) -> (a,0) x * lim(x,y) → (a,0) ln y...

Suppose I define sets D_n = \lbrace x \in [0,1] | x has an n-digit long binary expansion \rbrace . Now consider \bigcup_{n \in \mathbb{N}} D_n. This is just the set of Dyadic rationals and therefore countable for sure. Now for the question: is this equal to \bigcup_{n = 0}^{\infty} D_n...

Find the Fourier transform of the unit rectangular distribution f(t) = 1 for ltl<1 else 0 Since e-iωt is zero except for t in ]-1;1[ it must be an integral over this interval. But should I take the boundaries as -1 and 1? Because they are not included in the interval where e-iωt is not zero but...

I made up this limit problems trying to understand something in chemistry, so they may not necessarily have any answer. I am not sure how to evaluate them analytically. Not sure how L'Hopital's Rule would work here either. (\lim_{V→50^{-}}-log(\frac{50-V}{10(V+50)}))...

Homework Statement Use the two path test to prove that the following limits do not exist.Homework Equations \lim_{(x,y)\rightarrow{(0,0)}}\frac{4xy}{3x^2+y^2} The Attempt at a Solution The book that I am using introduces the Two Path Test theoretically but does not show an example of how to do...

Homework Statement find the limit: \lim_{x\rightarrow\frac{\pi}{6}}\frac{2sin(x)-1}{6x-\pi} The Attempt at a Solution Any starters please, I've tried the substitution method but went nowhere.I did x=(pi+h)/6. I still get 0 over something which is zero and i know that is not correct.

Homework Statement solve the limit: \lim_{x\rightarrow1}\frac{sin(x-1)}{\sqrt{x}-1} The Attempt at a Solution Is there a way of how i can solve this without using l'hospital's rule or taylor series?

Homework Statement solve the limit: \lim_{x\rightarrow0}\frac{2cos^{2}(x)-cos(x)-3}{x^{2}} The Attempt at a Solution Ok so i factored out the numerator, but i don't know where to go from there any help please...

Homework Statement find the limit of : \lim_{x\rightarrow0}\frac{\sqrt{5-cos(x)}-2}{x^{2}} Homework Equations The Attempt at a Solution I multiplied the numerator and the denominator by the conjugate of the numerator and i got : \frac{1-cos(x)}{x^{2}(\sqrt{5-cos(x)}+2)} then: i divided...

Homework Statement find ∫x/√(x+1).dx with limits 1 & 0 using substitution x = u^2 -1 Homework Equations The Attempt at a Solution dx = du x = u^2 -1 u = √( x+1) sub limits of 1 & 0 into u. Hence new limits of √2 & 1 Therefore, ∫ u^2 -1/ u = ∫ u - 1/u =...

Homework Statement lim(x,y)->(1,0) of ln((1+y^2)/(x^2+xy)) Homework Equations The Attempt at a Solution Used two paths, x=1 y=0 both gave my lim=0 so I tried x=rsin y=rcos, in attempt to use ε-δ to prove it. got to ln((1+r^2sin^2)/(r^2cos(cos+sin))) not sure where to go...

Homework Statement solve the following limit: \lim_{x\rightarrow0}\frac{x+sinx}{2x-sin3x}The Attempt at a Solution I know the principle of solving all sorts of limits but not trig limits, and since we just started trig limits it's still not clear to me, but i think to solve it we have to...

Homework Statement Find ∫e^x/ (1+e^2x). dx , with limits ln 2 & 0 given u= e^x Homework Equations The Attempt at a Solution u= e^x du/dx = e^x dx= du/e^x sub limits of ln2 & 0 → u Hence, limits 2 & 1 Therefore, ∫u* (1+e^2x)^-1* du/e^x = ∫ u/ (u + e^3x) = ∫...

[b]1. Homework Statement Evaluate ∫ 3x /(3x+1)^2.dx , with limits 1 & 0 using the sustitution u = 3x+1 Homework Equations The Attempt at a Solution u= 3x+1 du/dx = 3 dx = du/3 Therefore, ∫ 3x*(u)^-2 * du/3 = ∫ x* (u)^-2 Since u = 3x +1 Therefore, x =...

For absolute value of x, f(x) = lxl To prove continuous, I can express it as a piecewise function of x if x>0 and -x if x<0 and then I can take the limit of each as x approaches 0 from the negative and positive sides. Both limits give zero, and f(0) gives zero, so continuity is...

i am very confused about these problems, my teacher is hard to understand. a)lim x^2+x+2/x^2-5x+6 ..x->3 b)lim (1/x)-1/x^2-1 ..x->1 c)lim x^2+2x-6/x^2+3x-2 ..x->2 d)lim x^2tanx ..x->0 e)lim x^2sec^2xcot^2x ..x->0 f)lim x^2sin(1/x) ..x->0 g)lim x^2/sin^2x...

Homework Statement Hey Everyone , i have 4 L'Hopital's rule problems that i am totally stuck on, and hints would be greatly appreciated. Ill just put all 4 here, and any help would be great. 1. lim x->a+ (cos(x)ln(x-a)) / ln(e^x - e^a) Okay, so with this one i determined that it has...

Here is the proof provided in my textbook that I don't really understand. Suppose that x' and x'' are both limits of (xn). For each ε > 0 there must exist K' such that | xn - x' | < ε/2 for all n ≥ K', and there exists K'' such that | xn - x'' | < ε/2 for all n ≥ K''. We let K be the larger...

Homework Statement Show that if bn→b, then the sequence of absolute values |bn| converges to |b|. Homework Equations The Attempt at a Solution I've been proving various properties of limits, including product of limits and sum of products, but have been having trouble making...

This problem I encountered in my photography forum. A new model of camera comes out with a much higher megapixel sensor (Nikon D800, 36mpix). I argue that such sensor will need new lenses to be meaningful. Others claim that a given lens performance (here resolution) is always utilized by a new...

I mean I know that because there are physical limitations that there has to be some kind of limitation, but it seems like it could in a way go on forever, like you could just keep learning and generalizing previous information or learning and sort of putting it in your subconscious or...

Homework Statement Question : lim_{x\rightarrow2}f(x)Homework Equations The Attempt at a Solution I am really very confused about this. I know limits are the "intended height of the function". So, what if the function is like this? I know for one that this is a function since it passed the...

Homework Statement Find the limit of f(x,y) = \frac{x^{2}-y^{2}}{\sqrt{x^{2}+y^{2}+81}-9} as (x,y) \rightarrow (0,0) The Attempt at a Solution Ok, I looked at the examples in the book, and it seems pretty straight forward... I first look at f(x,0) to see what happens as we approach...

Homework Statement see attachment Homework Equations limx->0(1+x)1/x=e The Attempt at a Solution step 1: take log in both sides of an=...(as in function). step 2: multiply and divide it by 2n inside the log. step 3: there are n terms in multiplication so substitute 2(of...

Everything that exists, had existed and will ever exist are all contained within the universe... (Leave out the parallel universes concept for now).. So that means our imagination also exists within the universe... I mean with our mind we think and our mind is contained within the...

Homework Statement http://www4c.wolframalpha.com/Calculate/MSP/MSP18091a03ad70feibdhb300005da572897hebg236?MSPStoreType=image/gif&s=52&w=143&h=42 Homework Equations lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x) The Attempt at a Solution I plugged in 2 for x and it was 0/0 so then I...

Hello! I am playing around with an equation (i.e. it's not a textbook question), and I arrived at the following problem: The equation is: A = -1*\sum_{i=1}^{N}*\log_{N}(P_{i})*P_{i} Pi is less than or equal to 1 and more than or equal to 0, and is a probability of finding an object in a...

Let f(x) = |x|/x a. What is the limit of f, as x approaches 0 from the right? b. What is the limit of f, as x approaches 0 from the left? c. Hence, what is the limit of f, as x approaches 0? ------------------------------ The best way to evaluate limits involving absolute values is to use...

In general I find in books that the path integral approach is an equivalent alternative of the hamiltonian approach for QFT (and for QT in general, but my concern is with QFT). There I usually find that this method is usually developed in a formal way and used to derive Feynman rules, gauge...

If you look at this text towards the very end they are dividing by 2. I don't see why.

Homework Statement http://prikachi.com/images/26/4273026B.gif Homework Equations The Attempt at a Solution I'm having problems in solving the limit which is shown on the gif file . As you see I use L'Hopital's rule 2 times and I get to a point when I should divide -sinx with sinx...

I'm working through rewriting the gamma function as an infinite product, but my question is just about a specific substitution that was made in my textbook. They took the equation: \Gamma_ n(z)=\int_0^n t^{z-1} (1-\frac{t}{n}) ^ndt for Re(z)>0 and n greater than or equal to 1. and made the...

When sketching a graph I'm told to assume that the expression: f(x) =( e^x)/x Tends towards the infinite as x tends towards the infinite. Can someone show me how to check this? Thanks

Fourier series of complex numbers with diffrent limits of integration? Dear all, i don't know how to simplify a COMPLEX NUMBER Fourier series with LIMITS OF INTEGRATION that are not complementary. I MEAN limits LIKE this X to -X being easy to solve and SIMPLIFY but Not X to -Y or...

I have the following doubts. Please help me get through them... (1) Is there any difference between the terms 'limit does not exist' and 'limit is not defined'? (2) For a limit to exist does it have to be a finite number? (3) When we do the algebra of limits as lim (x->a) [f(x) + g(x)]...

Homework Statement If \lim_{x\rightarrow 0+}f(x)=A and \lim_{x\rightarrow 0-}f(x)=B find \lim_{x\rightarrow 0+}f(x^{3}-x) Homework Equations The Attempt at a Solution I don't have one. I am dumbfounded. Mostly i have been trying to understand the meaning of the composite...

In the last year or so, there has been a breeder arms race to produce the hottest pepper. The peak has gone up a little over 1 million scoville to over 1.5 million scoville in a short time. Since pure capsaicin is 16 million scoville, there is a well defined upper limit. I don't know the...

Homework Statement Find \int^{2}_{1}x^{-2}dx. Hint: Choose x^{*}_{i} to be the geometric mean of x_{i-1} and x_{i} (that is, x^{*}_{i} = \sqrt{x_{i-1}x_{i}}) and use the identity \frac{1}{m(m+1)} = \frac{1}{m} - \frac{1}{m+1} The Attempt at a Solution First off I am very confused by...

Homework Statement I have a limit problem, however I do know how to work limits, I guess what I need is more of a refresher on how to work third degree polynomials. The polynomial(s) I am trying to work with are the following: x3-2x2+2x-15 -and- x3-5x2+10x-12 The limit is a limit where x...

Can anyone suggest me a self study book for limits and continuitsy whic starts from zero level to a very advanced level thanks in advance rithu

i guys, I'm stuck on wording of a homework assignment and thought you might be able to help me. There are several questions... Consider the geometric series: (Sum from k=0 to infinity) of ar^k and consider the repeating decimal .717171717171 for these problems: Question 1: Find a formula...

Homework Statement Interpret the integrals (from 0 to 4)∫ (3x/4) dx + (from 4 to 5)∫ (sqrt(25-x^2)) dx as areas and use the result to express the sum above as one definite integral. Evaluate the new integral. Homework Equations The Attempt at a Solution I see that I could...

Okay so I've been teaching myself (with the aid of the mighty internet & several friends) algebra & now calculus. I have found that I didn't do too good at high school for various reasons. Some good...some not good. Anyway... I have a (what is probably a basic question) about factoring limit...

Homework Statement My professor gave us this problem: Convert the limit to an integral: \lim_{n\rightarrow inf} \frac{1}{n}(\sin(\pi/2) + \sin(\pi/2) + ... + \sin(\pi)) he said it was right endpoint from [0,π] then he set Δx = \frac{\pi}{n} then \lim_{n\rightarrow inf}...

Hi, If k_3 \cdot (A_1 \cos k_1 x + A_2 \sin k_1 x)\cdot(B_1 \cos k_2 y + B_2 \sin k_2 y)\cdot(C_1 e^{k_3 z}-C_2 e^{-k_3 z})=E in the limit as \sqrt{x^2+y^2+z^2}\rightarrow\infty Can we infer anything about any of the constants?

I'm trying to design my first switching regulator circuit. I require three voltage rails, 5V, 3.3V and 1.8V. But to get started, I'm just focusing on 1.8V. I've decided to use the LT3507 as it seems to be commonly available here. It also has 3 buck regulator outputs, so it's a one-chip solution...

Homework Statement Find volume bounded by: x - z = 0; x + z = 3; y + z = 1; z = y + 1; z = 0 Homework Equations Vol = \int\int\int_{V}dV The Attempt at a Solution I really don't know how to begin this problem because I have trouble visualizing what all those intersection of...

Homework Statement The Attempt at a Solution When I do the integral of this function I'm unsure of what the limits are. Anyone care to help? Thanks