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MAT A02– CÁLCULO A (atualizada em 2009.1)

LISTA DE EXERCÍCIOS( Questões de Provas Ia UNIDADE)
Limite
⎧ x2, x < −1
⎪
1) (2000 – 1) Considere a função de domínio IR, definida por f ( x) = ⎨− x + 1 , − 1 ≤ x < 1 .
⎪ log x, x ≥1
⎩
1.1) Esboce o gráfico de f .
1.2) Determine se existirem: lim f ( x) , lim f ( x) , lim f ( x) , lim f ( x) e lim f ( x) . x→ − ∞

2) (2000 – 1) Considerando f ( x) =

x→ + ∞

x→ − 1

x→ 0

x→ 1

x2 + x

, analise qual o domínio em que f (x) define uma função, x esboce o gráfico desta função no seu domínio de definição, e determine, se existirem, os limites lim f ( x) , lim f ( x) e lim f ( x) . x → 0−

x→ 0+

x→ 0

3) Calcule, se existirem, os seguintes limites:
⎛1⎞
3.1) (2000 – 1) lim ⎜ ⎟ π x→ ⎝ 2 ⎠

tgx

3.2) (1999 – 1) lim

x→ − 3

x+3 x −3 −6

3.3) (2000 – 1) lim

x→ 1

2

1 ⎤
⎡ 1
−
lim ⎢
3⎥
x → 1+ ⎣1 − x 1 − x ⎦

3.4) (1999 – 2)

3.6) (2000 – 1) lim

x→ 0

9+ x −3 x 3.8) (1999 – 2) lim ( x − x 2 + 1) x→ + ∞

x2 −3

3.10) (1999 – 2) lim

x→ + ∞ 3

3.12) (1999 – 1) lim

x2 −3

x→ + ∞ 3

3.14) (1999 – 2)

lim

x→ − 1

x3 +1

3.5) (1999 – 2) lim

x→ 0

3.7) (2000 – 1)
3.9) (1999 – 2)

3.13) (1999 – 2)

8x 3 + 1

2 x −1 x3 − x

3.15) (2000 – 1)

x 3 − 3x + 2

1 + x + x 2 −1 x lim

x 2 +1 − 2

x→ 1

3x 2 − 3x

lim ⎡ln ( x 2 + 2 + x )⎤
⎥⎦
⎢⎣

x→ − ∞

3

3.11) (2000 – 1)

x 2 − 7x + 6

lim

x→ + ∞

lim

x → − 5+

lim

x→ − 1

9 − x6 x3 +1
5− x

x + x − 20
2

3x 2 + x − 2 x3 +1
1

3.16) (2000 – 1) lim

x→ 0

3.18) (2000 – 1) lim

1 − cos x

tg 2 x + sen 2 x x→ 0 x sen x sen x
3.19) (1999 – 1) lim x→ π x − π
1⎤
⎡ 1 sen ⎥
3.21) (2000 – 1) lim ⎢ x⎦ x → 0 + ⎣ ln x
3.17) (1999 – 1)

x2 tgx − sen x

x3 cos x
3.20) (2000 – 1) lim x→+ ∞ x
⎛ ⎛⎜ 2− x 2 ⎞⎟
⎞
⎜
⎟
⎜
⎟
⎜ ⎝ 1+ x ⎠
⎟
3.22) (1999 – 2) lim ⎜ π cos (ln x) ⎟ x→ + ∞
⎜
⎟
⎜
⎟
⎝
⎠ x→ 0