- Calcolare il limite

z ltz' -Caicolare _n-oo ^lim {i*:l _{\ n/}

nm ltnl)":esiha

n-m \ n/

- Calcolare il limite

sen(r -

lim eT"-:f:-.

c+31-

sen(r-3\

lim e\":rz- : [m ,:eÌi# ;5 : _*oo.

c+3+ c+3+

I - Dimostrare per induzione

/. ^{1 \} "* '" ^ton lr+r) ^{n*-1 los (r+t )^}

{1+-l :e'"'"e\'r-)/:e'" '"b\''n,

- ^*oo.

\ n,/ n+m

/- r17 rrn-1

t ^1"S (G"/J ¹ n!, per ogni n c N ,n ) L

(r- (iÍC)n ^{< nr."-} (}[C ^{1 nt 2 <nt(n+ 1)} : (rz+ 1)l p€r ?? : 1 la disuguaglianza diventa 1 : 1

(.- (#"))' : _(to* (#"))"-'.'(1Í") ^{( n!iog} _(iÍ")

senl3z) 2 - Caicolare _r-O lim * _{br -f} t' ^'

,. ^senú Iim_-1, ,+o t

,.. - sen(3r) _{,.-_-} sen(32) 3 ³

IlfIl -=:llm-

r-oSxixz u-o 3x 5-rr 5