======T3======
[[http://wolframalpha.com/examples/Limits.html|Vypočítejte]] limitu posloupnosti:
=====22.=====
\( \lim_{n \to \infty} \frac{5 - 2n}{3n - 7} \)
[[wa>lim (5 - 2n) / (3n - 7) as n->infinity]]

=====23.=====
\( \lim_{n \to \infty} \frac{n^2 + 4}{n + 4} \)
[[wa>lim (n^2 + 4) / (n + 5) as n->infinity]]

=====24.=====
\( \lim_{n \to \infty} \frac{n^2}{n^3 + 5} \)
[[wa>lim (n^2) / (n^3 + 5) as n->infinity]]

=====25.=====
DELETEME \( \lim_{n \to \infty} \frac{(2n - 1)(n^2 - n + 2)}{(n + 1)(2n + 1)(3n + 1)} \)
[[wa> limit of ( (2n - 1)(n^2 - n + 2)) / ((n + 1)(2n + 1)(3n + 1)) as n=+oo ]]

=====26.=====
DELETEME \( \lim_{n \to \infty} \frac{n!}{(n + 1)!  - n!} \)
[[wa>lim n! / ((n + 1)! - n!) as n->infinity]]

=====27.=====
DELETEME \( \lim_{n \to \infty} n^{\sin \frac{1}{n}} \)
[[wa>lim (n^(sin (1/n))) as n->infinity]]

=====28.=====
DELETEME \( \lim_{n \to \infty} \frac{(-2)^n + 3^n}{(-2)^{n+1} + 3^{n+1}} \)
[[wa> lim ((-2)^n + 3^n) / ((-2)^(n+1) + 3^(n+1)) as n->+oo ]]

=====29.=====
\(\lim_{n \to \infty} \frac{2n + \sin n}{3n - 1} \)
[[wa>lim (2n + sin n) / (3n - 1) as n->infinity]]

=====30.=====
DELETEME \( \lim_{n \to \infty} \frac{\sqrt[3]{n^2} \sin n!}{n + 1} \)
[[wa>  lim ( cuberoot (n^2) sin n! ) / (n + 1) as n->+oo ]]

=====31.=====
\( \lim_{n \to \infty} ( \sqrt{n^2 + 2n} - n ) \) 
[[wa> lim sqrt(n^2 + 2n) - n   as n->infinity ]]

=====32.=====
\( \lim_{n \to \infty} ( \sqrt{n + 1} - \sqrt{n} ) \)
[[wa> lim sqrt(n + 1) - sqrt(n) as n->infinity]] Answer: 0 {{YMAT2:T32.png|StepByStep Solution}}
resp. lze použít racionalizace jako v [[#31]]

=====33.=====
DELETEME \( \lim_{n \to \infty}  \frac{1 + a + a^2 + \dots + a^n}{1 + b + b^2 + \dots + b^n}, |a| < 1, |b| < 1 \)

=====34.=====
DELETEME \( \lim_{n \to \infty} ( \frac{1}{n^2} + \frac{2}{n^2} + \dots + \frac{n-1}{n^2} ) \)

=====35.=====
DELETEME \( \lim_{n \to \infty} \sqrt{2} \sqrt[4]{2} \sqrt[8]{2} \dots \sqrt[2^n]{2} \)

=====36.=====
\( \lim_{n \to \infty} ( \frac{n + 4}{n + 3})^n \)
[[wa> lim ((n + 4)/(n + 3))^n as n->infinity]] {{YMAT2:T36.png|StepByStep}}

=====37.=====
\( \lim_{n \to \infty} (\frac{n - 3}{n})^n \)
[[wa> lim ((n - 3)/n )^n as n->infinity]]
upravíme na:
[[wa> lim (1 - 3/n)^n as n->+oo]] {{YMAT2:T37.png|StepByStep}}