Sketch the curves of the given functions by addition of ordinates. $y=3-2 \cos x$

Sketch the curves of the given functions by addition of ordinates. $y=\sin x+\sin 2 x$

Describe two advantages of using credit cards.

What curves are represented by the following? Sketch them. [0, t, t³]

Find the area of the region bounded by the curves y = x^2 + 2, y = x, x = 0 and x = 3.

Find the area between the curves. $y=x^{2}-30, \quad y=10-3 x$

Display the curves of the given functions on a calculator. $y=2 \sin x-\cos 2 x$

Use algebraic methods to find as m as many intersection points of the following curves as possible. Use graphical intersection points of the following curves as possible. Use graphical $r=1-\sin \theta$ and $r=1+\cos \theta$

Mark the statement True or False (T/F). Justify each answer.

When two Bezier curves are connected with G$^1$ geometric continuity, then the tangent vectors for the two curves at the common control point have the same direction.

Find the lengths of the curves. $x=y^{2 / 3}, 1 \leq y \leq 8$

Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.

$$\begin{gather*} (x + 3)y'' + xy' + (\ln |x|)y = 0, \,\,\, y(1) = 0, \,\,\, y'(1) = 1 \end{gather*}$$

Sketch the shifted exponential curves. $y=1-e^{x} \text { and } y=1-e^{-x}$

Use the method of the previous example to find a general expression for the slope of a tangent line to each of the indicated curves. Then find the slopes for the given values of $x$. Sketch the curves and tangent lines.

$$y = x^2 + 3x + 2\pi; x = -3, x = 3$$

Graph the curves $y=x^n$, $0 \leqslant x \leqslant 1$, for $n=0,1,2,3$, $4, \ldots$ on a common screen. By finding the areas between successive curves, give a geometric demonstration of the fact that

$$\sum_{n=1}^{\infty} \frac{1}{n(n+1)}=1$$