Exercicios Resolvidos de Limites Trigonometricos

Exercicios Resolvidos de Limites Trigonometricos

(Parte 1 de 3)

Limites Trigonométricos Resolvidos Sete páginas e 34 limites resolvidos

Usar o limite fundamental e alguns artifícios :1lim0=

1 fi xsenxx

1. x x senlim

= ?à x

0fi x senlim

0fi= 0

0 , é uma indeterminação.

x x senlim

0fi x sen 1lim 0fi = x x senlim

0fi

= 1 logo x x senlim

0fi

2. x

4senlim

0fi = ? à x

4senlim

=4.1= 4logo

senlim 0fi x x

4senlim 0fi =4

= ? à=

5senlim 0fi sen

4. nxmxx senlim

0fi = ? à nxmxx senlim 0fi = mxmxnmx sen.lim senlim

0fi = n m .1= n m logo nxmxx senlim 0fi = n m

5. x x 2sen

3senlim

0fi

= ? à x x 2sen

3senlim 0fi = = fi x x x x x

2 2senlim

3 3senlim x x senlim fifi t t y t y=

2 3 logo x x 2sen

6. sennxsenmx x 0limfi

= ? à nxmx x sen senlim 0fi = nx x x sen sen lim 0fi = nx nxn mx mxm sen.

lim 0fi = nx mx nm x sen sen

.lim 0fi = n m Logo sennxsenmx x 0limfi = n fi xtgx x 0

lim ?à =

fi xtgx x 0lim 0 fi xtgx x 0 fi x x cossen fi x 1.cos senlim0 x x x cos

1.senlim

0fi = x x x cos fi xtgx x 0 lim1

atga= 0

0 à Fazendo î íì fi

at à()t

ttg atga

Limites Trigonométricos Resolvidos Sete páginas e 34 limites resolvidos

9. x x x x x x x x x x x à 0lim fix x x x x x

= ?à 30

xtgxx -fi senlim x xtgxx-fi= x x

1.senlim xtgx sen x x cos.sensen x x x x x cos1 cos1.cos x x x x

senlim x xtgxx -fi = 2 sen11 lim xtgxx xtgx xtgxxx x x x x sen11 senxtgx xtgxx xtgx xtgx sen11 lim

12. ax ax --fi sensenlim= ? à ax ax --fi sensenlim= sen2 lim ax axax ax = ax = acos Logo ax --fi sensenlim= cosa

Limites Trigonométricos Resolvidos Sete páginas e 34 limites resolvidos xaxa sensenlim0 -+fi xaxa sensenlim0 xax xax æfi axaa a = xcos Logo ()a xaxa sensenlim0 -+fi

=cosx xaxa coscoslim0 -+fi xaxa coscoslim0 -+fi= xaxxax sen2 lim0 = aax

2 sen axa = xsen- Logo xaxa coscoslim0 -+fi

=-senx

15. ax ax --fi secseclim= ? à ax ax --fi secseclim= ax cos1cos1 lim= cos.cos coscos lim=

(Parte 1 de 3)

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