Define a sequence by a1=1a1=1 and an+1=(1−1(n+1)2)anan+1=(1−1(n+1)2)an for n≥1n≥1. Show that the limit exists and find the limit. I've shown that the limit LL exists by showing it's decreasing and bounded below by 00, but I'm not sure...
How to find the limit of functions in calculus. Step by step examples, videos and short definitions in plain English. Calculus made clear!
But I've never listened to Arabic or African music, I think it's very cool to find out that I like it. […] There's like a combination of new technology that hasn't been all that impossible to learn, and an interest in broadening a so-called normal music interest to like listen ...
How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution. This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, t...
Add a comment 1 Solve the derivate fxl = 0 for x without considering the interval. Filter the solutions to keep only those within your interval: [lim_inf, lim_sup]. Something like this: import sympy as sp x = sp.symbols('x') fx = (0.00282*x**4) + (0.206*x**3) - (...
To see how this function is related to our problem, notice that f(x)=∑n=0∞(−1)nxn2=∑n=0∞(x4n2−x4(n+1)2)g(4n+1,x).f(x)=∑n=0∞(−1)nxn2=∑n=0∞(x4n2−x4(n+1)2)g(4n+1,x). We prove that liminf and limsup of f(x)f(x) as x↑1...
I am trying to prove equation (6.3) in the lemma below. This is part of a course in calculus of variations, but that is irrelevant here, this is actually a question about the liminf and the inf of sequences Definition Consider the definition Let (X,d) be a me...
limx→1−∑n=0∞(−1)nxn2=12? The power n2n2 is problematic. Can we bring this back to the study of usual power series? I do not really have any idea for the moment. real-analysis sequences-and-series limits Share Cite Follow Follow this question to rece...