Analiza 1 - ćwiczenia SIMR 2010/2011 ćw 1 - 2 godz.
Temat: Ciąg, granica ciągu
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
n2 + (-1)n
(g) an =
n2 + (-n)n
n + cos n
(h) an =
n + sin n
"
n
(i) an = 2n + 7n
n+(-1)n
(j) an =
n
" "
(k) an = n2 + n - n2 - n
" "
" "
n2+ n+1- n2- n-1
" "
(l) an =
n+1- n
"
3
(m) an = n( n3 + 1 - n)
2. Obliczyć granicę ciągu lim an
n"
n-1
n2 + 3n
(a) an =
n2 + 4
2n2
-4
n3 + n - 1
(b) an =
n3 + 4
n-3
n + 2n2
(c) an =
n + n2 - 1
n2
-3
n3 + 2n - 1
(d) an =
n3 + 3n2 - n
(e) an = n(ln(n + 3) - ln n)
n-1
n2 + 3n
(f) an =
n2 + 4
2n2
-4
n3 + n - 1
(g) an =
n3 + 4
 2n+1
"
n2 + n
(h) an = "
3
n2 + n
n-3
n + 2n2
(i) an =
n + n2 - 1
n2
-3
n3 + 2n - 1
(j) an =
n3 + 3n2 - n