Maths I

In: Business and Management

Submitted By jmqd1995
Words 888
Pages 4
´
SOLUCIO
Soluci´ provisional Examen Setembre 2009-10 o 1. (a) Trobeu l’equaci´ d’una circumfer`ncia que passi pels punts (0, 2), (2, 0) i (4, 2). o e
(b) Trobeu el valors de k que fan que aquesta equaci´ sigui d’una circumfer`ncia, i en aquest o e cas indiqueu-ne el centre i el radi: x2 − 2kx + y 2 − 4y = −20
´
SOLUCIO
(a) (x − 2)2 + (y − 2)2 = 4.
(b) k > 4 o k < −4; centre (k, 2), radi



−16 + k 2 .

2. Digueu a quines funcions corresponen les seg¨ents gr`fiques, sabent que una s’obt´ a partir u a e d’una exponencial de la forma Aax i l’altra ´s un polinomi. Cal donar l’expressi´ de cada e o funci´ en la forma f (x) = ... o 3

2

1

-5

-4

-3

-2

-1

0

1

2

3

4

5

-1

-2

-3

´
SOLUCIO
3x
1
2 ∗ 2 i 2 (x − 2)(x − 3)(x + 1).
3. La capacitat de producci´ el`ctrica d’una central va ser l’any 2000 de 1000 unitats, o e
(a) Quant tardar` la producci´ a ser igual a 2000 unitats, si la producci´ augmenta un 3% a o o anual?
(b) Si la producci´ augment´s en 50 unitats anuals, quant tardar` a ser superior a 2000 o e a unitats? Plantegeu i resoleu aquest apartat usant desigualtats.
´
SOLUCIO
(a) 1000(1.03)t = 2000 → t = 23.44
(b) 1000 + 50t > 2000 → t > 20.
1

1
1−x2

4. Donada la funci´ f (x) = o (a) Calculeu l’aproximaci´ quadr`tica en x = 0. o a
(b) Useu aquesta aproximaci´ per a trobar el valor aproximat de o 100
.
99

´
SOLUCIO
(a) 1 + x2
(b) Si fem
5. (a) Calculeu

100
99

=

￿￿

1
1−x2

x10 +

obtenim x = 0.1 i per tant

1 x2 + 4ex + 1 +

100
99

√ ￿ x3 dx

= 1 + 0.12 ≈ 1.01

(b) Calculeu l’`rea tancada entre la funci´ f (x) = −(x − 2)(x + 2) i l’eix de les x. a o
´
SOLUCIO
(a)

x11
11

+

−1 x + 4ex + x +

(b)


￿

2
5



x5 + C

2

−2

x2 + 4 dx = −[

x3
32
− 4x]2 =
−2
3
3

6. (a)…...

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