5: Section 2.2 Answers
- Page ID
- 103620
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. \(2x^{3}y^{2}=c\)
2. \(3y\sin x+2x^{2}e^{x}+3y=c\)
3. Not exact
4. \(x^{2}-2xy^{2}+4y^{3}=c\)
5. \(x+y=c\)
6. Not exact
7. \(y\sin^2 x-xy+2e^{xy^2}=c\)
8. \(2y^{2}\cos x+3xy^{3}-x^{2}=c\)
9. Not exact
10. \(x^{3}+x^{2}y+4xy^{2}+9y^{2}=c\)
11. Not exact
12. \(\ln |xy|+x^{2}+y^{2}=c\)
13. Not exact
14. \(x^{2}+y^{2}=c\)
15. \(x^{2}y^{2}e^{x}+2y+3x^{2}=c\)
16. \(x^{3}e^{x^{2}+y}-4y^{3}+2x^{2}=c\)
17. \(x^{4}e^{xy}+3xy=c\)
18. \(x^{3}\cos xy+4y^{2}+2x^{2}=c\)
19. \(x\ln x+y\ln x-y=c\)
20. \(y=\frac{x+\sqrt{2x^{2}+3x-1}}{x^{2}}\)
21. \(y=\sin x-\sqrt{1-\frac{\tan x}{2}}\)
22. \(y=\left(\frac{e^{x}-1}{e^{x}+1} \right)^{1/3}\)
23. \(y=1+2\tan x\)
24. \(y=\frac{x^{2}-x+6}{(x+2)(x-3)}\)
25. \(y^2(1-x^2)-\cos^2 x=3\)
26. a. \(M(x,y)=2xy+f(x)\)
b. \(M(x,y)=2(\sin x+x\cos x)(y\sin y +\cos y)+f(x)\)
c. \(M(x,y) = ye^{x}-e^{y}\cos x+f(x)\)
27. a. \(N(x,y)=\frac{x^{4}y}{2}+x^{2}+6xy+g(y)\)
b. \(N(x,y)=\frac{x}{y}-2\cos x+g(y)\)
c. \(N(x,y)=x(\sin y+y\cos y)+g(y)\)
29. \(B=C\)
30. \(B=2D,\quad E=2C\)