Geometria
DEPARTAMENTO DE MATEMÁTICA
CÁLCULO A
1A LISTA DE EXERCÍCIOS
01. Esboce o gráfico de f, determine
3 x − 2,
a) f ( x ) = 2
,
4 x + 1,
x >1 x =1 x −2
a) f ( x ) =
b) f ( x ) =
3− x
− 2 x , x < −2
05. Calcule os limites a seguir ,
a) lim ( − y 5 − 3 y 4 + 12 y 2 ) y→ −1
d)
lim
x→ π / 2
g) lim
2x 2 + 3x − 2
8x − 1
3
x→1 / 2
j)
lim
y→ −1
sen x
1 + cos x
1− y2 y + 2+ y
x −2 x →8 x − 8
b) lim (log w − ln w ) w→10 e) lim
x→ 2
4
3
−1
h) lim e( x − 16 )( x − 8 ) x→ 2
k) lim
x→ 4
3
m) lim
x2 − 4
2−x
n) lim
x →1
3− 5+ x
1− 5 − x
3 3x + 5
c) lim e x ( x 3 − 4 ) x→1 f) lim
x3 − 1 x −1
i) lim
x −1 x−1 x→1
x→1
l) lim
x→ 4
x −2 x−4 −2
x 2 −1
06. Determine, se possível, as constantes a, b e c ∈ R, de modo que f seja contínua em x0 , sendo:
1
bx 2 + 2, x ≠ 1
a) f ( x ) =
b 2
, x =1
3 x − 3 , x > -3
b) f ( x ) = ax
, x = -3
bx 2 + 1 , x < -3
(x0 = 1)
(x0 = - 3)
07. Esboce o gráfico de cada função f a seguir, e determine o que se pede:
ln x , x > 0
a) f ( x ) = x
e , x ≤ 0
• lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ), x → −∞
x→ 0 +
x→ 0 -
x→ 0
x→1
x→ -1
x→ e
lim f ( x )
x → +∞
• intervalos onde f é contínua.
( 1 / 2 ) x , x > 0
b) f ( x ) =
1 / x , x < 0
• lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ), lim f ( x ) x → 0−
x→ − ∞
x →0 +
x →0
x→1
x→ −1
x→+ ∞
log1 / 2 x , x > 0
c) f ( x ) = 0
, x=0
−2
, x -3
f)
x→ −∞
c) lim f ( x ) = 3 e lim f ( x ) = 1 , sendo f ( x ) =
d) lim
3 ( x 2 −1 ) −1
x→ +∞
e) lim ( x 2 − 3x + x )
11. Calcule as constantes de modo que: x 2 − ax + b
a) lim
=5
b) x→ 3 x−3 x → +∞
c) lim ( 1 / π )x
ax 3 + bx 2 + cx + d
4 (x 2 + x