Hm talvez depois

1. Encontre o limite usando os teoremas de limite.
(a) lim (3x − 7)

(b) lim (2x2 − 4x + 5)

(c) lim (x3 + 8)

(d) lim

x→5

x→3

x→−2

x→3

2x + 1
2 − 3x + 4 x→−1 x

(f) lim

(e) lim
(g) lim

x→4

3

4x − 5
5x − 1

x→2

x2 − 3x + 4
2x2 − x − 1

(h) lim

x→−3

2. Encontre o limite. x2 − 49
(a) lim x→7 x − 7
4x2 − 9
(c) lim x→−3/2 2x + 3

x2 + 3x + 4 x3 + 1
3

5 + 2x
5−x

x2 − 25 x→−5 x + 5
3x − 1
(d) lim x→1/3 9x2 − 1
(b) lim

3x2 − 17x + 20 x→4 4x2 − 25x + 36
√
x−1
(g) lim x→−3 x − 1
√
3 x+1−1 (i) lim x→0 x

x2 − 9 x→−3 2x2 + 7x + 3
√
x+5−2
(h) lim x→−1 x+1
3
2x − 5x2 − 2x − 3
(j) lim 3 x→3 4x − 13x2 + 4x − 3

(e) lim

(f) lim

3. Seja f a fun¸˜o definida por ca 
 x2 − 9 se x = −3 f (x) =
 4 se x = −3
(a) Encontre lim f (x) e mostre que lim f (x) = f (−3). x→−3 x→−3

(b) Fa¸a um esbo¸o do gr´fico de f . c c a 4. Fa¸a um esbo¸o do gr´fico da fun¸˜o f e encontre, se existir, lim+ f (x), c c a ca x→a lim f (x) e lim f (x); se n˜o existir, indique a raz˜o. a a
−

x→a

x→a

1

(a) a = 1;

f (x) =


 2



se x < 1

−1 se x = 1





−3 se x > 1

 x + 4 se x ≤ −4
(b) a = −4; f (x) =
 4 − x se x > −4

 x2 se x ≤ 2
(c) a = 2; f (x) =
 8 − 2x se x > 2

(d) a = 1;

f (x) =


 2x + 3 se x < 1


4




3
(e) a = ;
2
(f) a = −1;

x2 + 2 se x > 1

f (x) = |2x − 3| − 4

 |x − 1| se x < −1

 f (x) =

(h) a = 0;

se x = −1

0




(g) a = 0;

se x = 1

|1 − x| se x > −1

|x| x 
 √−x se x ≤ 0
3
f (x) =
3
 √x se x > 0

f (x) =

5. Seja f a fun¸˜o definida por ca 
 2x − a se x < 3

 f (x) = ax + 2b se − 3 ≤ x ≤ 3



b − 5x se x > 3
Encontre os valores de a e b, tais que existam os limites: lim f (x) e lim f (x).

x→−3

x→3


 x2 + 3 se x ≤ 1
6. Dada f (x) =
 x + 1 se x > 1

e


 x2 se x ≤ 1 g(x) =
 2 se x >