Let $x_1,x_2,x_3...$ be all consecutive positive roots of the equation $\tan x = x.$ Find $\lim_{n \rightarrow \infty}(x_n-x_{n-1}).$
100735
$x_n$ is the $n$'th positive solution to $x=\tan(x)$. Find $\lim_{n\to\infty}\left(x_n-x_{n-1}\right)$
142778
Finding $\lim_{n\to\infty}a_n$ if $a_0=a,a_1=b$ and $a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$ where $a, b \in \mathbb{R}$
26783
If $(1+\sqrt{2})^n=a_{n}+b_{n}\sqrt{2}\;,(\forall n\in \mathbb{N}).$Then $\lim_{n\rightarrow \infty}\frac{a_{n}}{b_{n}} = $
83634
Find $\lim_{n\to \infty}\sqrt[n]{3^n+5^n}$
61328
Resolve $\lim_{x \to 0} \frac {\tan 3x}{\tan 5x}$
103218
Find $\lim_{(x,y) \to (0,0)} \frac{\tan(x^3+y^3)}{\sin(x^2+y^2)}$
149549
Infimum of $n$-th root of $n$
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
51804
How to show that a root of the equation $x (x+1)(x+2) ....... (x+2009) = c $ can have multiplicity at most 2?
104272
Inequality of $\vert \text{tanh}(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$
135774
Alternating roots of $f(x) = \exp(x) \sin(x) -1$ and $\exp(x)\cos(x) +1$
43703
Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $
64860
Evaluation of $\lim\limits_{x\rightarrow0} \frac{\tan(x)-x}{x^3}$
81537
Limit: $\lim_{x\to 0}\frac{\tan3x}{\sin2x}$
73478
Show that the equation $a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx} = 0$ has at most $n - 1$ real roots.
57573
Evaluate $ \lim_{n\to \infty} ( \lim_{x\to0} (1+\tan^2(x)+\tan^2(2x)+ \cdots + \tan^2(nx)))^{\frac{1}{n^3x^2}} $
115367
Limits with cubic root without L’Hopital’s Rule: $\lim_{x\to 1}\frac{\sqrt[3]{x}-1}{x-1} $