Calculo a

Universidade Federal do Esp´ ırito Santo
Centro de Ciˆncias Agr´rias e a
Lista 1 de C´lculo A a Professor: Thiago Louren¸o Pires c 1a Quest˜o: Explique com suas palavras o que significam as express˜es abaixo. a o
(a) lim f (x) = 5

(b) lim g (x) = 0

(c) lim h(x) = +∞

x→+∞

x→2

x→3+

2a Quest˜o: Dado que a lim f (x) = 5

lim g (x) = 0

x→a

lim h(x) = 8,

x→a

x→a

encontre, se existir, os limites. Caso n˜o existam explique por quˆ. a e
(b) lim [f (x)]3

(a) lim f (x) + g (x) x→a x→a

h(x)
(c) lim x→a f ( x ) f (x) − 2h(x)
(e) lim x→a g (x)

(d) lim

x→a

3

h(x)

f (x) − h(x) x→a f ( x ) + g ( x )

(f) lim

3a Quest˜o: Um aluno apressado de c´lculo A fez a seguinte conta: a a x2 + x − 6
(x + 3)(x − 2)
=
=x+3 x−2 (x − 2)
Explique, se existir, qual o erro da express˜o acima. Ap´s isso explique porque a equa¸˜o abaixo a o ca est´ correta. a x2 + x − 6
(x + 3)(x − 2)
= lim
= lim x + 3 = 5. x→2 x→2 x→2 x−2
(x − 2) lim 4a Quest˜o: Calcule os limites, se existirem. a (a) lim x2 + x − 6 x→2 t2 + t + 1

(c) lim

t →2

(e) lim π 2 + π + 1 x→4 x2 − 9 x→−3 2x2 + 7x + 3 x2 + 5x + 4
(i) lim 2 x→−4 x + 3x − 4

(g) lim

(2 + x)3 − 8 x→0 x

(k) lim

x4 − 16 x→2 x − 2

(m) lim
(o) lim

t →0

1
1
−2 t t +t

(9 + t)−1 − 9−1 t →0 t (q) lim

(b) lim (x + 3)(x − 2) x→1 (d) lim

x→2

x4 + 3x + 8

(4 + h)2 − 16 h→ 0 h 9−t
√
(h) lim t →3 3 − t x3 − 1
(j) lim 2 x→1 x − 1
√
x+2−3
(l) lim x→7 x−7
(f) lim

1
+1
(n) lim 4 x x→−4 4 + x
√
6−x−2
(p) lim √ x→2 3−x−1
√
x−3−1
(r) lim x+2 x→0+

|x − 4| x−4 |x − 4|
(u) lim x→4 x − 4
1
(w) lim 2 x→1 x − 1
1
(y) lim
−x
x→0

|x − 4| x−4 |x − 2|
(v) lim x→2 x − 2
1
(x) lim x→0+ x
1
(z) lim
− x−8 x→8 (s) lim

(t) lim

x→4+

x→4−

5a Quest˜o: Use o teorema do Sandu´ a ıche para mostrar que:
(a) lim x2 cos x = 0 x→0 (b) lim