Find the points of intersection (if any) of the given pair of curves and draw the graphs. y = 3x + 8 and y = 3x - 2

Sketch the curves of the given trigonometric functions.Check each using a calculator. $y=3 \cos (2 \pi x+\pi)$

Find the area between the curves. $y=2 x^{3}+x^{2}+x+5, \quad y=x^{3}+x^{2}+2 x+5$

Find the area between the curves. $x=-2, \quad x=1, \quad y=2 x^{2}+5, \quad y=0$

Find parametric equations for the curves given. -The hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{9}=1$.

Find the area of the region under the curves given.

$$y=t \sqrt{t^{2}+9} \text { on }[0,4]$$

Find the length of the following curves. $y=3 \ln x-\frac{x^{2}}{24}$, for $1 \leq x \leq 6$

Sketch the curves of the given functions by addition of ordinates. $y=\frac{1}{2} x-\cos \frac{1}{3} x$

Find the area of the region bounded by the given curves. $y=1 / x, \quad y=x^{2}, \quad y=0, \quad x=e$

(a) Graph some representative integral curves of $f ( x ) = x$ . (b) Find an equation for the integral curve that passes through the point ( 4,7 ) .

Find the length of the following curves. $y=\ln (x-\sqrt{x^{2}-1})$, for $1 \leq x \leq \sqrt{2}$

Sketch the curves of the given trigonometric functions.Check each using a calculator. $y=8 \sin \frac{\pi}{4} x$

Find the following points of the intersection. The point(s) of intersection of the curves $y=4 \sqrt{2 x}$ and $y=2 x^{2}$.

Find the following points of intersection. The point(s) of intersection of the curves $y=4 \sqrt{2 x}$ and $y=2 x^{2}$