16.9: Capítulo 16 Ejercicios de revisión

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Page ID: 116694

Edwin “Jed” Herman & Gilbert Strang
OpenStax

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¿Verdadero o Falso? Justifica tu respuesta con una prueba o un contraejemplo.

1. El campo vectorial$\vecs F(x,y) = x^2 y\,\mathbf{\hat i} + y^2 x\,\mathbf{\hat j}$ es conservador.

Contestar: Falso

2. Para el campo vectorial$\vecs F(x,y) = P(x,y)\,\mathbf{\hat i} + Q(x,y)\,\mathbf{\hat j} $, si está$P_y(x,y) = Q_z(x,y)$ en región abierta$D$, entonces$\displaystyle \int_{\partial D} P \,dx + Q \, dy = 0.$

3. La divergencia de un campo vectorial es un campo vectorial.

Contestar: Falso

4. Si$curl \, \vecs F = \vecs 0$, entonces$\vecs F$ es un campo vectorial conservador.

Dibuja los siguientes campos vectoriales.

5. $\vecs F(x,y) = \dfrac{1}{2}\,\mathbf{\hat i} + 2x\,\mathbf{\hat j} $

Contestar: $Un campo vectorial en dos dimensiones. Se muestran todos los cuadrantes. Las flechas son más grandes cuanto más alejadas del eje y se vuelven. Señalan hacia arriba y hacia la derecha para valores x positivos y hacia abajo y a la derecha para valores x negativos. Cuanto más alejados del eje y están, más pronunciada es la pendiente que tienen.$

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