SIMR Analiza 1, zadania: Granice ciągów
1. Obliczyć granicę ciągu lim an
n"
n2 + 3n
(a) an =
2n2 + 4
(b) an = n4 - 40n2 + n
n2 - 4n
(c) an =
n4 + 6
n4 - 4n
(d) an =
2n - n3
"
n - 4n + 1
(e) an =
n + 3
"
n2 - n4 + n3
(f) an =
n + 7
"
n
(g) an = 2n + 7n
2. Obliczyć granicę ciągu lim an
n"
n+(-1)n
(a) an =
n
" "
(b) an = n2 + n - n2 - n
" "
" "
n2+ n+1- n2- n-1
"
"
(c) an =
n+1- n
"
3
(d) an = n( n3 + 1 - n)
ëÅ‚ öÅ‚n
n2 + 1
íÅ‚ Å‚Å‚
(e) an =
2n2 + n
2n + 4n6
(f) an =
3n + n
n32n + n9n
(g) an =
(n + 1)32n + n56n