Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
7th Edition
ISBN: 9780134119281
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Chapter B, Problem 18SB

In Problems 5-28, determine whether each sequence converges or diverges. If it converges, find its limit.

{ a n } = { 10 + 1 n }

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(4) (8 points) (a) (2 points) Write down a normal vector n for the plane P given by the equation x+2y+z+4=0. (b) (4 points) Find two vectors v, w in the plane P that are not parallel. (c) (2 points) Using your answers to part (b), write down a parametrization r: R² — R3 of the plane P.
(2) (8 points) Determine normal vectors for the planes given by the equations x-y+2z = 3 and 2x + z = 3. Then determine a parametrization of the intersection line of the two planes.
(3) (6 points) (a) (4 points) Find all vectors u in the yz-plane that have magnitude [u also are at a 45° angle with the vector j = (0, 1,0). = 1 and (b) (2 points) Using the vector u from part (a) that is counterclockwise to j, find an equation of the plane through (0,0,0) that has u as its normal.
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