Limiti

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ANALISI MATEMA TICA 1 Prof. E.Maluta LIMITI DI SUCCESSIONI 1. limn!+1 n°2n2 3n2+ p n 2. limn!+1 n ≥ n2+1 n°2n3+3 ¥ 3. limn!+1 ° n1/3°n1/2¢ 4. limn!+1 n1/3+n1/6 1+n1/2 5. limn!+1 nlog n+1 n2+2 6. limn!+1 nlog n2+2 n+1 7. limn!+1 n3+n2 en/2 8. limn!+1 n!°en n10+ logn 9. limn!+1 ( p n)1/n 10. limn!+1 ( p nlogn)1/n 11. limn!+1 nlog n+1 n+2 12. limn!+1 p n·log ° 1+ 3 n ¢ 13. limn!+1 n2 ≥ 1°cos 3 n ¥ 14. limn!+1 n ≥ 3 n+1 n2+1 °1 ¥ RISUL T ATI: °2/3;°1/2;°1;0+;°1;+1;0+;+1;1+;1+;°1; 0; 9/2; log 3. 4.Esercizi sui limiti 1)Calcolare i seguenti limiti a)limx→1!ln"2x−1#"2x"2$ b)limx→0sin x"3x x2"cos x c)limx→1−"1 2#1/"x−1# d)limx→1−ln1/3"1−x2# e)limx→0!ln"1−3x 3−x #$−1 f)limx→01x 1−cos x 2 g)limx→0sin x−cos x"1x cos x h)limx→0 sin5x xs i n"4x# i)limx→""1x#x l)limx→"" 1 ln"x"3##x"2 m)limx→−""2x−3 x"5#x n)limx→0ex"sin x−1x o)limx→"""3x"2 3x"1#x p)limx→"x!ln"x"1#−ln x$ q)limx→eln x−1x−e r)limx→"""x x"2# x−2 2 s)limx→−1 2 − |2x"1|"x"2# 2x2"x t)limx→#" 2x−2|x| 1−|x| u)limx→0 1−cos"x3# x2"1"x−1# v)limx→1ln4 x"3−2 x−1 2)Calcolare il seguente limite al variare di$reale limx→0" xs i n"x2# "1−cos x#$ 3)Calcolare i seguenti limiti a)limx→"""ln"1"e−x# arctgx"Ch(-x)) b#limx→%/2"x"sin x# c#limx→0−" 1 arctgx"1x# d#limx→0""ln x"tg"x"% 2## e#limx→"""x1/%"cos x# f)limx→0 sin 3x"3x"x2 x g)limx→0 x−x2 sin x h)limx→"" x3"x2 x2"x−1 i)limx→"! x"1 x2"1 l)limx→"!ex"x2 x3 m)limx→2 x−2 x2−4x"4 n)limx→2 x−2 x2−4x"4 o)limx→"! xl nx"x2 x2 p)limx→"! x2"x"1−x x"1 4)Calcolare i seguenti limiti a!limx→0""ln x!5"1"x!2 b)limx→0"x1−#ln x c)limx→−!x3"1 2 !x d)limx→0" sin1x"2 x e)limx→3sin#x x−3 f)limx→0"ln x−ln"sin 3x!! 5)Calcolare i seguenti limiti a)limx→"!1xcos x b)limx→0$xs i n1x c)limx→−!e3xarctgx2−x cos x"2 d)limx→"0 cos x ln x 6)Calcolare i seguenti limiti a)limx→"!"1 2!2−x#ln"1"1x!−1$ b)limx→0 "−x!3/5…