Aula no 4 e 5
Limites
a) A figura representa o gráfico da função f .
y
3
y = f (x)
2
1
−2 −1
−1
1
2
3
x
−2
Calcule, caso existam, os seguintes limites:
(a)
lim f (x)
(b)
x→−∞
lim f (x)
(c)
x→−1
lim f (x)
(d) lim f (x)
(e)
x→2
x→2−
lim f (x)
x→+∞
b) Determine, caso existam, os seguintes limites :
x3 − 1
x→1 x − 1
(b) lim
(a) lim
(d)
x→1
2x2 + 1
x→+∞ 3x2 + 5x
(e)
x2 − 3x
x→3 5x − 15
(h) lim
lim
(g) lim
2
4 − x2
(c) lim
x→0 x3
x−2
− 10x + 31x − 30
5x3 − 2x
x→+∞ −2x2 + 10
(f )
5x4 − 2x3 + 3
x→+∞ x5 − 2x + 1
x4 − 16
x→2 (x − 2)2
(i)
lim
lim
lim
x→−2 x3
x2 + x − 2
+ 2x2 + x + 2
c) Considere a função f definida por:
⎧
⎪
3s3 − 3s se s > 1
⎪
⎪
⎨
f (s) =
3
se s = 1
⎪
⎪
⎪
1
⎩
se s < 1
s2
Calcule, caso existam, os seguintes limites:
(a) lim f (s)
s→1
(b) lim f (s)
s→0
(c)
lim f (s)
s→1+
(d)
lim f (s)
s→−∞
d) Use as informações que se seguem para calcular os limites pedidos.
lim f (x) = 2
x→c
lim g(x) = 3
x→c
5
lim h(x) = 27
x→c
(e)
lim
s→+∞
f (s)
s−1
(a) lim 5g(x)
x→c
(e) lim
x→c
3
h(x)
(b) lim [f (x) + g(x)]
x→c
(d) lim
(g) lim [h(x)]2
(h) lim [h(x)]2/3
x→c
h(x)
x→c 18
(f ) lim
x→c
6
f (x)
g(x)
(c) lim [f (x)g(x)]
x→c
x→c