91影视

For each function f and value x = c in Exercises 35鈥�44, use a sequence of approximations to estimate $f^{\text{'}}\left(c\right)$. Illustrate your work with an appropriate sequence of graphs of secant lines.

role="math" localid="1648705352169" $f\left(x\right)=e^x,c=0$

Find the angle between the diagonal of a cube and an adjoining edge of the cube.

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

$P(4,鈭�2),Q(鈭�2,0),R(1,鈭�5)$

(Hint: Think of the $xy$-plane as part of ${\mathrm{鈩�}}^3$.)

Show that the planes given by 2x 鈭� 3y + 5z = 7 and 鈭�6x + 9y 鈭� 15z = 8 are parallel, and find the distance between the planes

determine whether the given pairs of lines are parallel, identical, intersecting, or skew. If the lines are parallel, compute the distance between them. If the lines intersect, find the point of intersection and the angle at which the lines intersect.

${\mathbf{r}}_1\left(t\right)=鉄�2t+6,-t+1,3t鉄�$

${\mathbf{r}}_2\left(t\right)=鉄�-4t+3,2t-1,-6t+2鉄�$

Show that the planes given by $2x鈭�3y+5z=7$ and $鈭�6x+9y鈭�15z=8$ are parallel, and find the distance between the planes.

In Exercises 37鈥�42, find $||\mathit{v}||$ and find the unit vector in the direction of v.

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

$P(1,6),Q(0,鈭�3),R(鈭�5,4)$

(Hint: Think of the $xy$-plane as part of ${\mathrm{鈩�}}^3$.)

Graph the quadric surfaces given by the equations in Exercises 41鈥�48.

$x^2=\frac{y^2}{9}+\frac{z^2}{9}$

Graph the quadric surfaces given by the equations

$x^2=\frac{y^2}{9}+\frac{z^2}{9}$