grandes-ecoles 2010 QIII.A

grandes-ecoles · France · centrale-maths1__psi Parametric curves and Cartesian conversion

We denote $\mathscr{C}$ the image in $\mathbb{R}^2$ of the application $$\gamma : \left[\frac{\pi}{4}, \frac{7\pi}{4}\right] \rightarrow \mathbb{R}^2, t \mapsto (\cos t, 2\sin t)$$
III.A.1) Represent $\mathscr{C}$. III.A.2) Specify the following topological properties of $\mathscr{C}$. a) Is it an open set of $\mathbb{R}^2$? b) A closed set? c) A bounded set? d) A compact? e) A convex set?

We denote $\mathscr{C}$ the image in $\mathbb{R}^2$ of the application
$$\gamma : \left[\frac{\pi}{4}, \frac{7\pi}{4}\right] \rightarrow \mathbb{R}^2, t \mapsto (\cos t, 2\sin t)$$

III.A.1) Represent $\mathscr{C}$.\\
III.A.2) Specify the following topological properties of $\mathscr{C}$.\\
a) Is it an open set of $\mathbb{R}^2$?\\
b) A closed set?\\
c) A bounded set?\\
d) A compact?\\
e) A convex set?

Paper Questions

QI.A QI.B QI.C QI.D QI.E QII.A QII.B QII.C QII.D QIII.A QIII.B QIII.C QIII.D