# VESP EXAMEN TIPO A

(1)

## VESP EXAMEN TIPO A

𝑥

𝑥

𝜕𝑀 𝜕𝑦

2 𝑦

𝑒𝑥 𝑥

𝜕𝑁 𝜕𝑥

1 𝑦

𝑒𝑥 𝑥

𝑒𝑥 𝑥2

𝜕𝑀 𝜕𝑦

𝜕𝑁 𝜕𝑥 𝜕𝑁 𝜕𝑥

𝜕𝑀 𝜕𝑦

1 𝑦

𝑒𝑥 𝑥

𝑒𝑥

𝑥2

2 𝑦

𝑒𝑥 𝑥

1 𝑦

𝑒𝑥

𝑥2

𝑥2+𝑦𝑒𝑥

𝑥2𝑦

𝑥

2

𝑥

𝜕𝑁 𝜕𝑥− 𝜕𝑀 𝜕𝑦

∫𝑑𝑥𝑥

2

𝜕𝑀 𝜕𝑦

2𝑥 𝑦

𝑥

𝜕𝑁 𝜕𝑥

2𝑥 𝑦

𝑥

𝜕𝑀 𝜕𝑦

𝜕𝑁 𝜕𝑥 𝜕𝑓

𝜕𝑥

𝜕𝑓 𝜕𝑦

2

(2)

3

2

3

### =

3 ∫ 𝑒

3 ∫𝑑𝑥3𝑥

(43𝑥2)𝑑𝑥+𝐶 𝑒3 ∫𝑑𝑥3𝑥

3

4 ∫ 𝑥(𝑥2)𝑑𝑥+𝐶

𝑥

(3)

(4)

1

2

1

2

2

2

1

2

1

1

2

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

(5)

2

2

𝑥𝑥

′′

𝑦

′′

′′

′′

′′

2

1

2𝑥

2

−2𝑥

1

2

3

3

−4

3

4

1

2𝑥

2

−2𝑥

3

−4

(6)

′′

∞𝑛=0

𝑛

𝑛

∞𝑛=1

𝑛

𝑛−1

′′

∞𝑛=2

𝑛

𝑛−2

∞𝑛=2

𝑛

𝑛−2

𝑛=1∞

𝑛

𝑛−1

∞𝑛=0

𝑛

𝑛

∞𝑛=2

𝑛

𝑛−2

𝑛=1∞

𝑛

𝑛

∞𝑛=0

𝑛

𝑛

2

0

𝑛=3∞

𝑛

𝑛−2

∞𝑛=1

𝑛

𝑛

∞𝑛=1

𝑛

𝑛

2

0

𝑘=1∞

𝑘+2

𝑘

∞𝑘=1

𝑘

𝑘

∞𝑘=1

𝑘

𝑘

2

0

𝑘=1∞

𝑘+2

𝑘

𝑘

𝑘

2

0

2

−4

2

0

𝑘+2

𝑘

𝑘

3

−4(2) (3)(2)

1

−4(2) 3!

1

4

−4(3) (4)(3)

2

−4(3) (4)(3)

−4 2

0

(4)2(3)

4!

0

5

−4(4) (5)(4)

3

−4(4) (5)(4)

−4(2) (3)(2)

1

(4)2(4)(2)

5!

1

6

−4(5) (6)(5)

4

−4(5) (6)(5)

(4)2(3)

4!

0

−(4)3(5)(3) 6!

0

7

−4(6) (7)(6)

5

−4(6) (7)(6)

(4)3(2)

5!

1

−(4)3(6)(4)(2)

7!

1

8

−4(7) (8)(7)

6

−4(7) (8)(7)

−(4)3(5)(3)

6!

0

(4)4(7)(5)(3)

8!

0

9

−4(8) (10)(9)

7

−4(8) (10)(9)

−(4)3(6)(4)(2)

7!

1

(4)4(8)(6)(4)(2)

(7)

0

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

0

2

2

4

3

6

4

8

𝑘

𝑘

2𝑘

1

3

2

5

3

7

𝑘

𝑘

2𝑘+1

𝑘

𝑘

𝑘

𝑘

(8)

## VESP EXAMEN TIPO B

3

𝜕𝑀 𝜕𝑦

2𝑥2 𝑦

𝑥

𝜕𝑁 𝜕𝑥

3𝑥2 𝑦

𝑥

𝑥

𝜕𝑀 𝜕𝑦

𝜕𝑁 𝜕𝑥

𝜕𝑁

𝜕𝑥

𝜕𝑀

𝜕𝑦

3𝑥2

𝑦

𝑥

𝑥

2𝑥2 𝑦

𝑥

𝑥2 𝑦

𝑥

𝑥2+𝑦𝑒𝑥 𝑦

3

3

𝑥

2

𝑥

𝜕𝑁 𝜕𝑥−

𝜕𝑀 𝜕𝑦

− ∫𝑑𝑥𝑥

−1

1 𝑥

2

𝜕𝑀 𝜕𝑦

2𝑥 𝑦

𝑥

𝜕𝑁 𝜕𝑥

2𝑥 𝑦

𝑥

𝜕𝑀 𝜕𝑦

𝜕𝑁 𝜕𝑥 𝜕𝑓

𝜕𝑥

𝜕𝑓 𝜕𝑦

2

(9)

3

4

5 ∫𝑑𝑥5𝑥

4

5

2

5 ∫

𝑑𝑥 5𝑥

5

4 ∫ 𝑥(𝑥2)𝑑𝑥+𝐶

𝑥

(10)

(11)

1

2

1

2

2

2

1

2

1

1

2

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

(12)

2

2

𝑥𝑥

′′

𝑦

′′

−1

′′

−1

′′

′′

2

1

2

−1

2

3

3

2𝑦

2

1

2

3

2𝑦

2

1

2

2𝑦

(13)

′′

∞𝑛=0

𝑛

𝑛

∞𝑛=1

𝑛

𝑛−1

′′

∞𝑛=2

𝑛

𝑛−2

∞𝑛=2

𝑛

𝑛−2

𝑛=1∞

𝑛

𝑛−1

∞𝑛=0

𝑛

𝑛

∞𝑛=2

𝑛

𝑛−2

𝑛=1∞

𝑛

𝑛

∞𝑛=0

𝑛

𝑛

2

0

𝑛=3∞

𝑛

𝑛−2

∞𝑛=1

𝑛

𝑛

∞𝑛=1

𝑛

𝑛

2

0

𝑘=1∞

𝑘+2

𝑘

∞𝑘=1

𝑘

𝑘

∞𝑘=1

𝑘

𝑘

2

0

𝑘=1∞

𝑘+2

𝑘

𝑘

𝑘

2

0

2

5

2

0

𝑘+2

𝑘

𝑘

3

(5)(2) (3)(2)

1

(5)(2) 3!

1

4

(5)(3) (4)(3)

2

### =

(5)(3)(5) (4)(3)(2)

0

52(3)

4!

0

5

5(4) (5)(4)

3

5(4) (5)(4)

(5)(2) 3!

1

52(2)(4) 5!

1

6

5(5) (6)(5)

4

5(5) (6)(5)

52(3) 4!

0

53(3)(5) 6!

0

7

5(6) (7)(6)

5

5(6) (7)(6)

52(2)(4)

5!

1

53(2)(4)(6)

7!

1

8

5(7) (8)(7)

6

5(7) (8)(7)

53(3)(5) 6!

0

54(3)(5)(7) 8!

0

9

5(8) (9)(8)

7

5(8) (9)(8)

53(2)(4)(6) 7!

1

54(2)(4)(6)(8)

(14)

0

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

0

2

2

4

3

6

4

8

𝑘

2𝑘

1

3

3

5

4

7

𝑘

2𝑘+1

𝑘

𝑘

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## Referencias

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