Lista 4

Propaganda
```Complementos de Matemática 1
Quarta Lista de Exercı́cios
1a Questão: Calcule os limites abaixo:
x2 −4
x−→2 x−2
(g)
9−x2
x−→−3 3+x
(b) lim (x2 + 2x − 1) (h)
lim x+1
3
x−→−1 x +1
(a) lim
x−→2
lim
(c) lim
(i) lim
(d)
x2 −5
3 +6
2x
x−→2
3 +8
lim xx+2
x−→−2
(j)
x2 +5x+6
2
x−→−3 x −x−12
(k)
x2 −x−6
2 −4x+3
x
x−→3
(l)
(e)
lim
(f ) lim
1−x
√
x−→1 1− x
√
√
2
lim x+2−
x
x−→0
√
lim 2− x4−x
x−→0
√
x
lim 3−
x−→9 9−x
2a Questão: Verifique se lim f (x) existe:
x−→a



2
se x &lt; 1


(a = 1)
(a) f (x) =
−1 se x = 1



 −3 se x &gt; 1

 x + 3 se x ≤ −2
(b) f (x) =
 3 − x se x &gt; −2



2x + 3 se x &lt; 1


(c) f (x) =
2
se x = 1



 7 − 2x se x &gt; 1

 |x − 1| se x 6= −1
(d) f (x) =
 0
se x = −1



x + 1 se x &lt; −1


(e) f (x) =
x2
se − 1 ≤ x ≤ 1



 2 − x se x &gt; 1
(a = −2)
(a = 1)
(a = −1)
(a = −1 e a = 1)
1
3a Questão: Calcule os limites abaixo:
(a)
3x2 −5
2
x−→+∞ 4x +2
(g)
(b)
x3 −1
3
x−→−∞ x +3
(h)
(c)
lim 2x+1
x−→+∞ 5x−2
(i)
(d)
lim x+4
2
x−→+∞ 3x −5
√
lim 3x 2x+2
x−→+∞ 4x +1
√
x2 +4
lim x+4
x−→+∞
(j)
(e)
(f )
lim
lim
4x3 +2x2 −5
3
x−→−∞ 8x +x+2
√
4
x +3x2
lim
3
x−→−∞q x +2
lim
x−→+∞
lim
x+3
2x−1
lim
x5/2 +3x2 +1
x3 +2x−1
x−→+∞
(k)
lim
√
x−→+∞
x2 + 1 − x
4a Questão: Calcule os limites abaixo:
(a)
(b)
(c)
lim x
x−→4− x−4
lim x
x−→2− 2−x
x2 +2
x2 −1
(h)
lim+
x−2
x2 −x
(i)
x−→0
(e)
(g)
lim+
x−→1
(d)
(f )
x
lim
2
x−→1+ −x +3x−2
√
2
lim− 3+x
x
x−→0
√
x2 −9
lim+ x−3
x−→3
2x3 −4
x−→+∞ 5x+3
lim
lim 2 x−3
x−→3− x −6x+9
5a Questão: Encontre as assı́ntotas verticais e horizontais e faça um esboço do gráfico das
funções abaixo:
(a) f (x) =
4
x−5
(e) f (x) =
(b) f (x) =
−3
(x+2)2
(f ) f (x) =
(c) f (x) =
1
x2 +5x−6
(g) f (x) =
(d) f (x) =
2x
x−1
√ 2
x2 −4
−3x
√
x2 +3
x2 +1
x2 −5x+6
6a Questão: Calcule os limites abaixo:
sin2 x
2
x−→0 3x
(a) lim
(e) lim
(b)
sin(4x)
x
x−→0
sin(9x)
lim
x−→0 sin(7x)
(f )
1−cos x
x2
x−→0
(g)
(c) lim
(d) lim
3x2
x
x−→0 1−cos2 ( 2 )
2
lim
1+
1 3x
x
lim
1+
1 x
3x
x−→+∞
x−→+∞
7a Questão: Determine se as funções abaixo são contı́nuas no ponto a indicado e, em caso
negativo, indique o tipo de descontinuidade:
(a) f (x) =
(b) f (x) =
x2 +x−6
x+3


x2 +x−6
x+3
(a = −3)
se x 6= −3
(a = −3)
 −5
se x = −3



1 + x se x ≤ −2


(c) f (x) =
2 − x se − 2 &lt; x ≤ 2



 2x − 1 se x &gt; 2
(d) f (x) =
9x2 −4
3x−2
(a = 32 )

 |x − 2| se x 6= −3
(e) f (x) =
 2
se x = −3
√
(f ) f (x) =
√
5+x− 5
x
(a = −2 e a = 2)
(a = 3)
(a = 0)
3
```