Find an equation for and sketch the graph of the level curve of the function ƒ(x, y) that passes through the given point.

$$f ( x , y ) = \frac { 2 y - x } { x + y + 1 } , \quad ( - 1,1 )$$

Use a calculator to evaluate the given expression to the nearest tenth of a degree.

$$\arccos (0.8425)$$

Mots utiles: se brosser, se coucher, s'en aller, s'endormir, s'habiller, se lever, se maquiller, se peigner, se raser, se reveiller

un peigne

Use the stated method with $d x=0.05$ to estimate $y(c)$ where $y$ is the solution to the given initial value problem.
improved Euler; $c=3 ; \quad \dfrac{d y}{d x}=\dfrac{x-2 y}{x+1}, \quad y(0)=1$

The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle.

$$11 \mathrm { km } , 60 \mathrm { km } , 61 \mathrm { km }$$

Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold.

All functions with period $2 \pi$.

Graph each inequality in the coordinate plane.

$$-5 \leq x+2 y \leq 9$$

(a) Let F be a field in which 1 + 1 = 0. Show that a + a = 0 for all a (this can also be written a = -a). (b) Suppose that a + a = 0 for some $a \neq 0$. Show that 1 + 1 = 0 (and consequently b + b = 0 for all b).

The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle.

$$10 \mathrm { yd } , 24 \mathrm { yd } , 26 \mathrm { yd }$$

Let

$$f(x, y)=x^2-2x^3+3xy$$

. FInd an equation of the level curve that passes through the point (-1, 1)

Compute the stated power of the given matrix:

$$A=\left[\begin{array}{rrr} 1 & -2 & 8 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{array}\right]$$

(b) $A^{-1000}$

In this exercise, find the equations of the tangent lines at the point where the curve crosses itself.

$$x=t^3-6 t, \quad y=t^2$$

Find an equation for the tangent line to the given curve at the point where $x=x_0$.

$$y=\frac{2 x-1}{1-x^3} ; x_0=0$$

Find an equation for the tangent line to the given curve at the point where $x = x_0. \quad y=\frac{x}{2 x+3} ; x_{0}=-1$