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Let x, y, z be the dimensions of the rectangular box. This gives a linear system in ci and c 2 which has a unique solution if the lines are not parallel. Note that coso smo cos a coso none of cos a, cos b, sin a, sin 6 are zero. Therefore this line coincides with a radius of the sphere that passes through the center of the cap and h is measured along this line. From part ba is also parallel to b – c. Since f”‘ x is decreasing on [4,4.

May not be scanned, copied, nr duplicnled. By Exercise 1 1. May nol be scanned, copied, or duplicated, or po. Alternatively, we can find the value of 9 and proceed as in Example 7. May not be scanned, copied, or duplicated, or posled lo a publicly accessible website, in whole or in part.

Because of differences between the regular version and the Early Transcendentals version of the text, some references are given in a dual format. Sinlilarly, as t increases from to 1, y decreases from 1 to 0 while x repeats its pattern, and we arrive back at the origin.

To find the region D: Let a be the area of the original triangle.

### Cálculo de Varias Variables – 6ta Edición – James Stewart – PDF Drive

May not be scanned, copied, or duplicated, or posted lo a publicly accessible website, stewatr whole or in pun. The tangent vector is normal to the normal plane, and the vector 6, 6, -8 is normal to the given plane.

The surface is a paraboloid of revolution circular paraboloid with vertex at the origin, axis the y-axis and opens to the right. For the interior of the region, we find the critical points: First we find – — implicitly by taking partial derivatives of both sides with respect to Ri: See the statement ofStok. Since the direction vectors 2, 3,4 and 6,-1, 2 aren’t parallel, neither are the lines. A unit vector in the direction of AB is i and a unit vector in the direction of AC is j.

Two nonzero vectors can’t be both parallel and orthogonal, so at least one of u, v must be 0. The cross product can also be used to find the area of a parallelogram determined by two vectors.

All Rights Reserved May rail be scanned, copied, nr duplicated, or posted to a publicly accessible website, in whole or in part. The plane contains the points a, 0, 00, b, 0 and 0, 0, c. This change gives us the upper half. So by Theorem 8, the series represents sinh x for all x.

So Ji x converges for all a; and its domain is -oo, oo. This is the equation of an ellipsoid: This means that as we move through the point 6, 4 in the direction of u, the temperature increases at a rate of approximately stewsrt. Muy not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in port.

## Cálculo de Varias Variables – 6ta Edición – James Stewart

Thus the only critical point is 2,1. Since we are minimizing the area of the ellipse, and the circle lies above the x-axis, the ellipse will intersect the circle for wolucionario one value of y. The boatman wants to reach the point 3, 2.

See 56and 7 in Section Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including.

Thus the critical points are 0, 1f0tt, -1f0and 2jt, 1. False; div F is a scalar field.

This is true by Fubini’s Theorem. In each theorem, we have an integral of a “derivative” over a region on the left side, while the right side involves the values of the original function only on the boundary of the region. Note that this is true no matter how R is divided into subrectangles.

## Cálculo de Varias Variables – James Stewart – 4ta Edición

May nol be scanned, copied, ur duplicated, m posted loa publicly accessible website, in whole or in part. Let r be the radius of one of the circles. We can approximate the directional nua at Homestead in the direction of the eye of the hurricane by the average rate of change of wind speed between the points where this line intersects the contour lines closest to Homestead. This is a three-leaved rose.

Thus the uja R in xyz-spaw corresponds to the region S in ttuu;-space consisting of the smaller piece of the. May not be scanned, copied, or duplicated, or pqacd to a publicly a www.

The surface appears to be a portion of a circular cylinder of radius 3 with axis the x-axis. All Rights Reserved May not Ik scanned, copied, or duplicated, or posted to a pvibiicly stewwart website, in whole or in part.

We make a table of values of 2-xy of as, y points near the origin. May not b wwvv. From the geometrical nature of the problem, this critical point must give an absolute maximum. By zooming in sewart using a cursor, we find that the lowest point is about 1. A finite number of terms doesn’t affect convergence or divergence of a series.