Limites trigonométricos resolvidos
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Limites Trigonométricos ResolvidosSete páginas e 34 limites resolvidos Usar o limite fundamental e alguns artifícios : senx =1 x→0 x lim
0 x x lim = , é uma indeterminação. =? à x →0 sen x x → 0 sen x 0 x 1 1 x lim = lim = = 1 logo lim =1 sen x x →0 sen x x →0 sen x x → 0 sen x lim x→0 x x sen 4 x sen 4 x sen 4 x 0 sen y à lim 4. = 4. lim = ? à lim = =4.1= 4 2. lim x →0 y →0 x→0 x→0 0 4x y x x sen 4 x lim =4 x→0 x sen 5 x 5 sen 5 x 5 sen y 5 sen 5 x = ? à lim . logo lim 3. lim = lim . = x →0 2 x x →0 2 y →0 2 x →0 2 x y 5x 2 1. lim 4. lim sen mx = x →0 nx sen 3 x x →0 sen 2 x 3 2
logo
=
5 2
? à lim
5. lim
=? à logo
6. lim
x→0
senmx = sennx
? à
sen mx m = x →0 nx n sen y sen 3 x sen 3 x sen 3 x lim 3. lim sen 3 x 3 y →0 y 3 x →0 3 x 3x = . lim = lim x = lim = . = .1 = sen t sen 2 x 2 x →0 sen 2 x x → 0 sen 2 x x→0 sen 2 x 2 lim lim 2. x→0 2 x t →0 t x 2x sen 3 x 3 lim = x →0 sen 2 x 2 sen mx sen mx sen mx m. sen mx x mx = lim m . mx = m lim = lim = lim Logo sen nx x →0 sen nx x →0 n sen nx x → 0 sen nx x →0 n n. nx nx x
sen mx m sen mx = lim . x →0 x→0 n nx mx
=
sen y m . lim n y →0 y
=
m m .1= n n
logo lim
senmx m = x → 0 sennx n lim
7.
8.
sen x 0 tgx tgx tgx sen x 1 lim = ? à lim = = lim cos x = lim . = à lim x→ 0 x x→ 0 x x→ 0 x x→ 0 x → 0 cos x x 0 x tgx sen x 1 sen x 1 =1 lim . = lim . lim = 1 Logo lim x→ 0 x→ 0 x → 0 cos x x→ 0 x x cos x x x → 1 0 tg (t ) tg a 2 − 1 tg a 2 − 1 = ? à lim 2 = lim à Fazendo t = a 2 − 1, à lim =1 2 a →1 a − 1 a →1 a − 1 t →0 t t →0 0
(
)
(
)
logo lim
tg a 2 − 1 a2 −1
(
a →1
) =1
1
Limites Trigonométricos Resolvidos
Sete páginas e 34 limites resolvidos 9. lim x − sen 3 x x + sen 2 x
x →0
= ? à lim
x →0
x − sen 3 x x + sen 2 x
=
0 0
à f (x ) =
x − sen 3 x x + sen 2 x
=
sen 3 x x.1 − x = sen 5 x x.1 + x
sen 3 x sen 3 x sen 3 x x.1 − 3. 1 − 3. 1 − 3. 3. x 3. x