# Respostas - Calculo A - Cap 5 d - Flemming e Gonçalves

5.14 – EXERCÍCIO – pg. 232 Determinar os seguintes limites com auxílio das regras de LHospital.

→ x x

3 - x

→ x x x

2lim x x −

34 x x x

5lim x

2lim lim x ex xe x x cos lim exxx x x e x e x x

2 lim 2pi x xsen

1lim 2 x x x x x x x x

lnlim x x x

→ xxgx x cos2cot lim

2/ pi pi cos cos2 cos cos2 lim cos2cot cotcos2lim

senx senxxxx xsenx x senx x senx x x xxg xgxx x x pipi pi pi pi

1 lim

1 limlim

x x x x x x x x x x x x x e e e e e e e e e e e e xsenh

coshlim0

→ x x

lim x x x x x x xtgx x 4cos1 2seclim

sec4sec4.sec.sec2lim xtgxxxtgxx xsen xxtgx x pi pi x x cos1

1coshlim

coshlimlim xsenh x

lim cos1lim cot

1 cos1lim x xsen xtg x xg x x x

1ln21ln lim

1 lnlim1 x x x x x x x x x x

1lim x

x x x x x x x x x

 ln3lim

lim ln4

 3lim

ln ln4 lnlimlnlimln exx x x x x x x x xsenx x→0 lim

1lim cos2lim cos lim cot.seccos 1lim cot.seccos

1 lim

1 lnlimln.lim lnlimlimln xxsenx xxsen x xsen xgxxxgx x xsen x xxsen xsen x xsenx xsen x

1 lim

e ex x x x x x x x x

1lim lim 1 lnlim ln 1 1limlnlimlnlimln

2 cos x x pipi

1lim

2 cos coslim xtgxxxtgx x x x pipipipi pi pi lim

2 cos lim

2 cos

2 cos

1lim senx x x sen x x senx x sen x x pipipi pipipipi pipi pi ex x

pipi pi pipipi x x x sen coslim

1 cos lim1 lim lim xsenh x ∞→ lim

coshlim x

lim x x x x x x

12coslim lim)2(cosln3lim

)2ln(coslim)2(coslimln e ex xsenxx x xsenxx x x xsen x x xsen x x x x xasen x→

cos.cos. .coscoslim cos coslim cos cos lim axxaxsenaxsen axsenxsenaxaxa xaxsen xsenaxa xsen x axsen axa x x

3lim

1lim

→→→ x x x x x x

39 - tgxxx

xsen xxxxg xtg x xtgxxx x tgxx tgx x

1lim seccos 1lim cot lnlim

1 lnlimlnlimlnlimlimln e x xxsenx xsen tgx x lim lim ln2 ln2limln ln2 2limlnlimlimln x x x x x x x x

2 seclim

2cos 1lim xsen x x xtgx xtg x x x ln lnlim +∞→ x x x x lim

1 lim

exe xe exe e x xe xex xexe x x x x x x x x x