Des amis sont au restaurant. Dites ce que chacun choisit.

un soda

un chocolat chaud

un steak-frites

une salade de tomates

un sandwich

une tarte aux pommes (apple pie)

1. Mélanie est végétarienne. Elle...

2. Nous avons tr$\`{e}$s faim. Nous...

3. Vous avez soif. Vous...

4. Tu n’as pas tr$\`{e}$s faim. Tu...

5. Pauline et Léa ont froid. Elles...

6. J’adore les desserts. Je...

Use a CAS to perform the following steps in this exercise.

a. Plot the space curve traced out by the position vector $\mathbf{r}$.

b. Find the components of the velocity vector $dr/dt$.

c. Evaluate $dr/dt$ at the given point $t_0$ and determine the equation of the tangent line to the curve at $\mathbf{r}\left(t_0\right)$.

d. Plot the tangent line together with the curve over the given interval.

$$\mathbf{r}(t)=\sqrt{2} t \mathbf{i}+e^t \mathbf{j}+e^{-t} \mathbf{k}, \quad-2 \leq t \leq 3, \quad t_0=1$$

Determine whether the relation is a function. Explain.

$$( - 4,8 ) , ( - 1,2 ) , ( 2 , - 4 ) , ( 5 , - 10 )$$

Convert the given time period to years, in fraction form, assuming a 360-day year (this assumption does not affect the number of quarters (4), months (12), or weeks (52) in a year].

12 weeks

Determine whether the statement is true or false. Justify your answer. The product of two binomials is always a seconddegree polynomial.

Find all points on the graph of $f(x)=x^{3}+9 x^{2}+19 x-10$ where the slope of the tangent line is $-5$ .

For the polynomial function $g(x)=2 x^{3}+5 x^{2}-28 x-15,$ Determine the maximum number of real zeros that the function may have.

For any two line segments that are congruent, what must be true about the lengths of the segments?

Write the equation in standard form. $2 y+3=-\frac{1}{3}(x-2)$

Find f(n) when

$$n = 2^k,$$

where f satisfies the recurrence relation f(n) = f(n/2) + 1 with f(1) = 1.

Find $y^{\prime}$ and the slope of the tangent line to the graph of each equation at the indicated point. $(1+y)^{3}+y=x+7 ;(2,1)$

For what values of c is the angle between the vectors $\langle 1,2,1\rangle$ and $\langle 1,0, c\rangle$ equal to $60^{\circ}$ ?

Find the first four terms of each sequence. $a_{n}=(-1)^{n+1}+n$

Use the definition of the derivative to find the slope of the tangent line to the graph of the function f(x)=4x+5 at any point P(x, f(x)) on the graph.