New posts in limits

Prove or disprove that if $\lim\limits_{x\to0^+}f(x)=0$ and $|x^2f''(x)|\leq c$ then $\lim\limits_{x\to0^+}xf'(x)=0$

real-analysis limits derivatives

Evaluate $\lim\limits_{n \to \infty} nx_n.$

real-analysis calculus sequences-and-series limits

Convergence of the function series $\sum \frac{n!}{(nx)^n}$ for $x<0$

sequences-and-series limits analysis exponential-function sequence-of-function

What is $\lim_{n\to\infty} n (\sum_{k = 1}^{n} \frac{1}{\sqrt {n^2 + k}} - 1)$?

calculus limits

Cubic addition and differentiablility

calculus limits derivatives

Calculate $\sum\limits_{i=0}^\infty(2^{2^{(-i)}}-1)$

sequences-and-series limits exponentiation

Evaluating $\sqrt{6+\sqrt{6+\cdots}}$

sequences-and-series limits nested-radicals

Is $ \lim_{n \to \infty} a_n ^{b_n} = e^{\lim_{n \to \infty}(a_n - 1)b_n}$ always true?

limits limits-without-lhopital

Limit of an integral (remainder term of a Euler-Maclaurin expansion)

real-analysis integration limits

Where did the negative answer come from in the continued fraction $1+\frac{1}{1+1/(1+\dots)}$?

calculus sequences-and-series limits continued-fractions

On a proof of Riesz-Fischer Theorem

real-analysis functional-analysis limits measure-theory proof-verification

Is the sequence defined by the recurrence $ a _ { n + 2 } = \frac 1 { a _ { n + 1 } } + \frac 1 { a _ n } $ convergent? [duplicate]

real-analysis sequences-and-series limits convergence-divergence recurrence-relations

Dominated convergence theorem for complex-valued functions?

real-analysis integration limits probability-theory convergence-divergence

E-N Definition of Limit with a minus in the denominator

limits

Is there a mathematical statement that is linking integer limits to real limits?

real-analysis limits elementary-number-theory real-numbers

Why is the ratio test for $L=1$ inconclusive?

sequences-and-series intuition limits convergence-divergence

Limit of the sequence $a_{n+1}=\frac{1}{2} (a_n+\sqrt{\frac{a_n^2+b_n^2}{2}})$ - can't recognize the pattern

sequences-and-series limits trigonometry recurrence-relations pattern-recognition

How to show $\lim_{n\to\infty}n\cdot \sum_{m=1}^{\infty}\Big(1-\frac{1}{m}\Big)^n\cdot \frac{1}{m^2}=1.$

real-analysis limits

Prove that $a_n=(-1)^n$ does not converge

sequences-and-series limits solution-verification

Integral of $1 / \sqrt x$ using Limits

calculus integration limits definite-integrals