Calculus with Analytic Geometry by edwards & Penney soln ch13

Calculus with Analytic Geometry

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -3-2-1123-2-112Section 13.2C13S02.001:Becausef(x, y) = 4−3x−2yis defined for allxandy, the domain offis the entiretwo-dimensional plane.C13S02.002:Becausex2+ 2y2=0 for allxandy, the domain off(x, y) =px2+ 2y2is the entiretwo-dimensional plane.C13S02.003:If eitherxoryis nonzero, thenx2+y2>0, and sof(x, y) is defined—but not ifx=y= 0.Hence the domain offconsists of all points (x, y) in the plane other than the origin.C13S02.004:Ifx6=ythen the denominator inf(x, y) is nonzero, and thusf(x, y) is defined—but not ifx=y. So the domain offconsists of all those points (x, y) in the plane for whichy6=x.C13S02.005:The real numberzhas a unique cube rootz1/3regardless of the value ofz. Hence the domainoff(x, y) = (y−x2)1/3consists of all points in thexy-plane.C13S02.006:The real numberzhas a unique cube rootz1/3regardless of the value ofz. But√2xis realif and only ifx=0. Therefore the domain off(x, y) = (2x)1/2+ (3y)1/3consists of all those points (x, y)for whichx=0.C13S02.007:Because arcsinzis a real number if and only if−15z51, the domain of the given functionf(x, y) = sin−1(x2+y2) consists of those points (x, y) in thexy-plane for whichx2+y251; that is, theset of all points on and within the unit circle.C13S02.008:Because arctanzis defined for every real numberz, the only obstruction to the computationoff(x) = arctan(y/x) is the possibility thatx= 0. This obstruction is insurmountable, and therefore thedomain offconsists of all those points (x, y) in thexy-plane for whichx6= 0; that is, all points other thanthose on they-axis.C13S02.009:For every real numberz, exp(z) is defined and unique. Therefore the domain of the givenfunctionf(x, y) = exp(−x2−y2) consists of all points (x, y) in the entirexy-plane.C13S02.010:Because lnzis a unique real number if and only ifz >0, the domain off(x, y) = ln(x2−y2−1)consists of those points (x, y) for whichx2−y2−1>0; that is, for whichy2< x2−1. This is the regionbounded by the hyperbola with equationx2−y2= 1, shown shaded in the following figure; the boundinghyperbola itself isnotpart of the domain off.C13S02.0011:Because lnzis a unique real number if and only ifz >0, then domain off(x, y) = ln(y−x)consists of those points (x, y) for whichy > x. This is the regionabovethe graph of the straight line withequationy=x(the line itself isnotpart of the domain off).1C13S02.012:Because√zis a unique real number if and only ifz=0, the domain of the given functionf(x, y) =p4−x2−y2consists of those points (x, y) for whichx2+y254. That is, the domain consistsof all those points (x, y) on and within the circle with center (0,0) and radius 2.C13S02.013:Ifxandyare real numbers, then so arexy, sinxy, and 1 + sinxy. Hence the onlyobstruction to computation off(x, y) =1 + sinxyxyis the possibility of division by zero. So the domain offconsists of those points (x, y) for whichxy6= 0;that is, all points in thexy-plane other than those on the coordinate axes....
View Full Document

This document was uploaded on 02/01/2008.

Page1 / 179

Calculus with Analytic Geometry by edwards & Penney soln ch13

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online