contables

Departamento de Ciencias B´
asicas
C´
alculo vectorial
Taller 3. Aplicaciones de Funciones vectoriales

1. La curva generada por la ecuaci´
on vectorial R(t) = t2ˆı + (t + 1)ˆ es:

A.

C.B.

D.

2. La curva generada por la ecuaci´
on vectorial r(t) = (3 cos(t), 4 sin(t)) es:

A.

C.

B.

D.

3. La ecuaci´
on de la recta√tangente, el vector unitario, la velocidad yla aceleraci´on para la curva
F (t) = (t sin(t), cos(t), 3t), en el punto t = 0 son:
√
√
A. L(t) = (0, 1, 0) + t(0, 0, 3), Tˆ = (0, 0, 1), v = (0, 0, 3), a = (2, −1, 0)
√
√
B. L(t) = (0, −1, 0)+ t(0, 0, 3), Tˆ = (0, 0, −1), v = (0, 0, 3), a = (2, 1, 0)
√
√
√
C. L(t) = (0, 1, 0) + t(0, 0, 3), Tˆ = (0, 0, 3), v = (0, 0, 3), a = (−2, −1, 0)
√
√
D. L(t) = (0, −1, 0) + t(0, 0, − 3), Tˆ =(0, 0, 1), v = (0, 0, − 3), a = (2, 1, 0)
4. La ecuaci´
on de la recta tangente, el vector unitario, la velocidad y la aceleraci´on para la curva
r(t) = (et , e−t ), en el punto t = 0 son:
A.L(t) = (−1, 1) + t(−1, 1), Tˆ =

√1 (−1, −1),
2

B. L(t) = (1, −1) + t(1, −1), Tˆ =

√1 (1, −1),
2

v = (1, −1), a = (−1, 1)

C. L(t) = (1, 1) + t(1, −1), Tˆ =

√1 (−1, −1),
2

v = (1,−1), a = (1, −1)

D. L(t) = (1, 1) + t(1, −1), Tˆ =

√1 (1, −1),
2

v = (−1, −1), a = (1, 1)

v = (1, −1), a = (1, 1)

5. La ecuaci´
on de la recta tangente, el vector unitario, la velocidady la aceleraci´on para la curva
ˆ en el punto t = 9 son:
F (t) = tˆı + tˆ + 32 t3/2 k,
A. L(t) = (t, t, 9 + 3t), Tˆ =

√

1
,
11(1,1,3)

v = (1, 1, t1/2 ), a(t) = (1, 1, 16 )

B. L(t) =(t, t, 9 + 3t), Tˆ =

√

1
,
11(1,3,1)

v = (1, t1/2 , 1), a(t) = (1, 1, 13 )

C. L(t) = (t, t, 9 + 3t), Tˆ =

√

1
,
11(1,1,3)

v = (1, 1, 9), a(t) = (t, t, 16 )

D. L(t) = (t,t, 9 + 3t), Tˆ =

√

1
,
11(1,1,3)

v = (1, 1, 3), a(t) = (0, 0, 16 )

6. La longitud de la curva r(t) = (cos(t), sin(t), cosh(t)) para t en el intervalo [0, ln 2] es:
A.

4
3

B....