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  1. \documentclass[a4paper,11pt]{article}
  2.  
  3. \usepackage{tkz-euclide}
  4.  
  5. % Custom made packages
  6. \usepackage{../../_sty/UNI} % Global exam seetings
  7. \usepackage{../../_sty/UiT} % University specific changes
  8. \usepackage{../../_sty/IMS} % Faculty specific changes
  9. \usepackage{../MAT-0001} % Course specific changes
  10.  
  11. % Always keep your main language last
  12. \usepackage[british]{babel}
  13.  
  14. %==============================================================================%
  15. % COURSE INFORMATION %
  16. %==============================================================================%
  17.  
  18. \UNIsetup{%
  19. Language = {norsk}, %auto = language defined by babel
  20. isExercise = {false},
  21. ExamType = {h}, % h=home exam
  22. includeSolution = {true},
  23. CourseCode = {auto}, % auto = \courseCode (defined in courseCode.sty, e.g. MAT-1001.sty)
  24. CourseName = {auto}, % auto = \courseName (defined in courseCode.sty, e.g. MAT-1001.sty)
  25. Year = {2021}, % No auto setting for this, as it might change on recompilation
  26. Month = {6}, % No auto setting for this, as it might change on recompilation
  27. Day = {2},% No auto setting for this, as it might change on recompilation
  28. StartHour = {9},
  29. DurationHours = {5}, % Set the number of hours the exam/exercise should last
  30. % DurationDays = {7}, % Set the number of days the exam/exercise should last
  31. % Location = {},
  32. ApprovedAids = {
  33. % \supportMaterialD
  34. \begin{supportMaterialList}
  35. \item Alle hjelpemidler er tillatt
  36. (egne notater, pdfer fra forelesningene, lærebok, internett etc).
  37. \end{supportMaterialList}
  38. },
  39. Pages = {auto},
  40. % Sheets = {Ruter},
  41. ContactID = {},
  42. Mobile = {Du \ kan \ ringe \ 776 20 880 \ for \ support \ på \ eksamensdagen},
  43. % willVisit = {false},
  44. % VisitWhen = {ca 11},
  45. }
  46.  
  47.  
  48. %==============================================================================%
  49. % OWN COMMANDS AND PACKAGES BELOW HERE %
  50. %==============================================================================%
  51.  
  52. \usepackage{colortbl}
  53. \usepackage{booktabs}
  54. \usepackage{tabularx}
  55. \usepackage{csquotes}
  56. \usepackage{polynom}
  57. \polyset{style=A}
  58. \usepackage{adjustbox}
  59. \usepackage[version=4]{mhchem}
  60.  
  61. \sisetup{per-mode=symbol}
  62.  
  63. \usepackage{circuitikz}
  64.  
  65. \ExplSyntaxOn
  66. \NewDocumentCommand\mylist{>{\SplitList{,}}m}
  67. {%
  68. \ProcessList{#1}{\myitem}%
  69. \firstitemtrue
  70. }
  71.  
  72. \newif\iffirstitem
  73. \firstitemtrue
  74. \newcommand\myitem[1]{
  75. \iffirstitem
  76. \firstitemfalse
  77. \else
  78. ${}+{}$%
  79. \fi
  80. $\textcolor{UiT-main}{#1}\thinspace\si{\percent}$}
  81. \ExplSyntaxOff
  82.  
  83. \usepackage{diagbox}
  84.  
  85. \usepackage{pgf}
  86. \usepackage{pgffor}
  87. \usepgfplotslibrary{fillbetween}
  88.  
  89. % This locks the seed
  90. \pgfmathsetseed{2020}
  91. \ExplSyntaxOn
  92. \sys_gset_rand_seed:n {34357}
  93. \ExplSyntaxOff
  94.  
  95. \makeatletter
  96. \def\pgfmathdeclarelist#1#2{%
  97. \def\pgfmath@list@name{#1}%
  98. \c@pgfmath@counta=0%
  99. \pgfmath@declarelistlist#2{\pgfmath@stop}%
  100. }%
  101. \def\pgfmath@declarelistlist#1{%
  102. \ifx#1\pgfmath@stop%
  103. \expandafter\edef\csname pgfmath@list@\pgfmath@list@name
  104. @length\endcsname{\the\c@pgfmath@counta}%
  105. \else%
  106. \advance\c@pgfmath@counta by1\relax%
  107. \pgfutil@namedef{pgfmath@list@\pgfmath@list@name @\the\c@pgfmath@counta}{#1}%
  108. \expandafter\pgfmath@declarelistlist%
  109. \fi%
  110. }
  111.  
  112. \def\pgfmathgetlistitem#1#2#3{\expandafter\let\expandafter#1\expandafter=\csname
  113. pgfmath@list@#2@#3\endcsname}
  114.  
  115. \def\pgfmathsetlistitem#1#2#3{%
  116. \pgfutil@namedef{pgfmath@list@#1@#2}{#3}%
  117. }
  118.  
  119. \def\pgfmathgetlistlength#1#2{%
  120. \expandafter\let\expandafter#1\expandafter=\csname
  121. pgfmath@list@#2@length\endcsname%
  122. }
  123.  
  124. \def\pgfmathknuthshuffle#1{%
  125. \pgfmathgetlistlength\pgfmath@len{#1}%
  126. \pgfmathloop%
  127. \ifnum\pgfmathcounter>\pgfmath@len%
  128. \else%
  129. \pgfmathrandominteger\pgfmath@temp{1}{\pgfmath@len}%
  130. \pgfmathgetlistitem\pgfmath@@temp{#1}{\pgfmathcounter}%
  131. \pgfmathgetlistitem\pgfmath@@@temp{#1}{\pgfmath@temp}%
  132. \def\pgfmath@marshal{\pgfmathsetlistitem{#1}}%
  133. \expandafter\pgfmath@marshal\expandafter{\expandafter\pgfmath@temp\expandafter}\expandafter{\pgfmath@@temp}%
  134. \expandafter\pgfmath@marshal\expandafter{\expandafter\pgfmathcounter\expandafter}\expandafter{\pgfmath@@@temp}%
  135. \repeatpgfmathloop%
  136. }
  137.  
  138. \makeatother
  139.  
  140. \usepackage{caption,subcaption}
  141. \renewcommand{\thesubfigure}{\textcolor{UiT-blue}{\Alph{subfigure}}}
  142.  
  143. % \newcommand{\trigonometricGraph}[1]{
  144. % \begin{tikzpicture}
  145. % \begin{axis}[
  146. % /pgf/declare function={
  147. % f(\x)=#1;
  148. % },
  149. % grid=major,
  150. % grid style={dashed,gray!30},
  151. % axis lines=middle,
  152. % enlargelimits=false,
  153. % inner axis line style={-stealth},
  154. % % unit~vector~ratio*=1 1 1,
  155. % % axis~line~style={draw=none},
  156. % % tick~style={draw=none}, % Remove axis line just for this plot
  157. % width=1.1\textwidth,
  158. % ytick={-20,-19,...,10},
  159. % xtick={
  160. % -6.28318, -4.7123889, -3.14159, -1.5708,
  161. % 1.5708, 3.14159, 4.7123889, 6.28318
  162. % },
  163. % xticklabels={
  164. % $-2\pi$, $-\frac{3\pi}{2}$, $-\pi$, $-\frac{\pi}{2}$,
  165. % $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$, $2\pi$
  166. % },
  167. % ymin=-1.2,ymax=1.2,
  168. % xmin=-3.3,xmax=5,
  169. % % xticklabel~style={anchor=north~east},
  170. % ]
  171. % \addplot+[mark=none,smooth,ultra~thick,UiT-blue] {f(x)};
  172. % \end{axis}
  173. % \end{tikzpicture}
  174. % }
  175. \ExplSyntaxOn
  176. \NewExpandableDocumentCommand \randomint { m m }
  177. { \int_rand:nn { #1 } { #2 } }
  178. %
  179. \NewExpandableDocumentCommand{\trigonometricGraph}{+m}{
  180. \begin{tikzpicture}
  181. \begin{axis}[
  182. /pgf/declare~function={
  183. f(\x)=#1;
  184. },
  185. grid=major,
  186. grid~style={dashed,gray!30},
  187. axis~lines=middle,
  188. enlargelimits=false,
  189. inner~axis~line~style={-stealth},
  190. % unit~vector~ratio*=1 1 1,
  191. % axis~line~style={draw=none},
  192. % tick~style={draw=none}, % Remove axis line just for this plot
  193. width=1.1\textwidth,
  194. ytick={-20,-19.5,...,10},
  195. xtick={
  196. -6.28318, -4.7123889, -3.14159, -1.5708,
  197. 1.5708, 3.14159, 4.7123889, 6.28318
  198. },
  199. xticklabels={
  200. $-2\pi$, $-\frac{3\pi}{2}$, $-\pi$, $-\frac{\pi}{2}$,
  201. $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$, $2\pi$
  202. },
  203. ymin=-1.2,ymax=1.2,
  204. xmin=-3.3,xmax=5,
  205. % xticklabel~style={anchor=north~east},
  206. ]
  207. \addplot+[mark=none,smooth,ultra~thick,UiT-blue] {f(x)};
  208. \end{axis}
  209. \end{tikzpicture}
  210. }
  211. %
  212. \NewExpandableDocumentCommand{\firstchar}{sm}
  213. {
  214. \IfBooleanTF{#1}
  215. {
  216. \grill_firstchar:V #2
  217. }
  218. {
  219. \grill_firstchar:n { #2 }
  220. }
  221. }
  222.  
  223. \cs_new:Nn \grill_firstchar:n
  224. {
  225. \int_compare:nTF { \tl_count_tokens:f { \tl_head:n { #1 } } > 1 }
  226. {% we have to redo
  227. \grill_firstchar:f { \tl_head:n { #1 } }
  228. }
  229. {% just one token
  230. \tl_head:n { #1 }
  231. }
  232. }
  233. \cs_generate_variant:Nn \tl_count_tokens:n { f }
  234. \cs_generate_variant:Nn \grill_firstchar:n { V, f }
  235. \ExplSyntaxOff
  236.  
  237. \usepackage{xspace}
  238. \usepackage{xstring}
  239. \newcommand{\girlName}{Lise\xspace}
  240. \newcommand{\boyName}{Nils\xspace}
  241.  
  242. \edef\boy{\firstchar*{\boyName}}
  243.  
  244. \usetikzlibrary{arrows, calc,intersections, decorations.pathmorphing}
  245. \tikzset{
  246. arrowMe/.style={postaction=decorate,
  247. decoration={markings, mark=at position .5 with {\arrow[thick]{#1}}
  248. } }}
  249.  
  250. \ExplSyntaxOn
  251. % Internals
  252. \int_new:N \l__nebu_min_prefix_int
  253. \tl_new:N \l__nebu_base_number_tl
  254. \tl_new:N \l__nebu_mode_tl
  255. \cs_new:Npn \nebu_prefix:n #1
  256. {
  257. \exp_args:Nf \__nebu_prefix:n
  258. { \exp_args:Nf \fp_to_scientific:n { \tl_lower_case:n {#1} } }
  259. }
  260. \cs_new:Npn \__nebu_prefix:n #1
  261. { \__nebu_prefix:nwnw #1 \q_stop }
  262. \cs_new:Npn \__nebu_prefix:nwnw #1 e #2 \q_stop
  263. { \__nebu_find_prefix:nnn {#2} {#1} {1} }
  264. \cs_new:Npn \__nebu_find_prefix:nnn #1 #2 #3
  265. {
  266. \tl_if_exist:cT { l__nebu_ #1 \tl_use:N \l__nebu_mode_tl _prefix_tl }
  267. {
  268. \use_i_delimit_by_q_stop:nw
  269. { \__nebu_output:nnn {#2} {#1} {#3} }
  270. }
  271. \int_compare:nNnT {#1} < \l__nebu_min_prefix_int
  272. {
  273. \use_i_delimit_by_q_stop:nw
  274. {
  275. \exp_args:Nf \__nebu_find_prefix:nnn
  276. { \int_eval:n { \l__nebu_min_prefix_int } } {#2}
  277. { #3 / 1\prg_replicate:nn { \l__nebu_min_prefix_int - #1 }{ 0 } }
  278. }
  279. }
  280. \use_i:nn
  281. {
  282. \exp_args:Nf \__nebu_find_prefix:nnn
  283. { \int_eval:n {#1-1} } {#2} {#3*10}
  284. }
  285. \q_stop
  286. }
  287. \exp_args_generate:n { fv }
  288. \cs_new:Npn \__nebu_output:nnn #1 #2 #3
  289. {
  290. \exp_args:Nfv \nebu_output:nn
  291. { \fp_to_decimal:n {#1*#3} } { l__nebu_ #2 \tl_use:N \l__nebu_mode_tl _prefix_tl }
  292. }
  293. \cs_new_protected:Npn \nebu_prefix_set:Nnn #1 #2 #3
  294. {
  295. \exp_args:Nxx \__nebu_prefix_set:nnN
  296. { \tl_trim_spaces:n {#2} } { \int_eval:n {#3} } #1
  297. }
  298. \cs_new_protected:Npn \__nebu_prefix_set:nnN #1 #2 #3
  299. {
  300. \tl_clear_new:c { l__nebu_ #2 _prefix_tl }
  301. \tl_clear_new:c { l__nebu_ #2 _siunitx_prefix_tl }
  302. \tl_set:cn { l__nebu_ #2 _prefix_tl } {#1}
  303. \tl_set:cn { l__nebu_ #2 _siunitx_prefix_tl } {#3}
  304. \int_set:Nn \l__nebu_min_prefix_int { \int_min:nn {#2} { \l__nebu_min_prefix_int } }
  305. }
  306. % User interface
  307. \NewExpandableDocumentCommand \prefix { m }
  308. { \nebu_prefix:n {#1} }
  309. \cs_new:Npn \nebu_output:nn #1 #2 { #1\, \textrm{#2} }
  310. \NewDocumentCommand \setprefix { m m m }
  311. { \nebu_prefix_set:Nnn #1 {#2} {#3} }
  312. \DeclareSIPrefix \none { } { 0 }
  313. \setprefix \none { } { 0 }
  314. %
  315. \cs_new_protected:Npn \__nebu_store:nn #1 #2
  316. {
  317. \tl_set:Nn \l__nebu_base_number_tl {#1}
  318. \cs_set:Npn \prefix {#2}
  319. }
  320. \NewExpandableDocumentCommand \prefixSI { o m o m }
  321. {
  322. \group_begin:
  323. \cs_set_eq:NN \nebu_output:nn \__nebu_store:nn
  324. \tl_set:Nn \l__nebu_mode_tl { _siunitx }
  325. \nebu_prefix:n {#2}
  326. \SI [#1] { \l__nebu_base_number_tl } [#3] {#4}
  327. \group_end:
  328. }
  329. \ExplSyntaxOff
  330.  
  331. \setprefix \yocto { y } { -24 }
  332. \setprefix \zepto { z } { -21 }
  333. \setprefix \atto { a } { -18 }
  334. \setprefix \femto { f } { -15 }
  335. \setprefix \pico { p } { -12 }
  336. \setprefix \nano { n } { -9 }
  337. \setprefix \micro { \SIUnitSymbolMicro } { -6 }
  338. \setprefix \milli { m } { -3 }
  339. \setprefix \centi { c } { -2 }
  340. \setprefix \deci { d } { -1 }
  341. \setprefix \deca { da } { 1 }
  342. \setprefix \hecto { h } { 2 }
  343. \setprefix \kilo { k } { 3 }
  344. \setprefix \mega { M } { 6 }
  345. \setprefix \giga { G } { 9 }
  346. \setprefix \tera { T } { 12 }
  347. \setprefix \peta { P } { 15 }
  348. \setprefix \exa { E } { 18 }
  349. \setprefix \zetta { Z } { 21 }
  350. \setprefix \yotta { Y } { 24 }
  351.  
  352. \NewDocumentCommand\brakpar
  353. {
  354. s % optional *
  355. m % first mandatory argument
  356. }
  357. {%
  358. \IfBooleanTF{#1}
  359. { \fpcompare{\fv{#2}=0}{ ) }{ ] } }
  360. { \fpcompare{\fv{#2}=0}{ ( }{ [ } }
  361. }
  362.  
  363. \NewDocumentCommand{\fphide}{ O{#2} m m }{%
  364. \fpcompare{#2=#3}{}{#1}%
  365. }
  366.  
  367. \NewDocumentCommand{\fpsimp}{ o m m m }{
  368. #2%
  369. \IfNoValueTF{#1}%
  370. {#3#4}%
  371. {\fphide[#3#4]{#1}{#4}}%
  372. }
  373.  
  374. \NewDocumentCommand{\fpdiv}{s m m }{%
  375. \IfNoValueTF{#1}{%
  376. \fpsimp[1]{#2}{/}{#3}}%
  377. {\fpcompare{#2=0}{}{\fphide[\fpsimp[1]{#2}{/}{#3}]{#2}{#3}}}%
  378. }
  379.  
  380. \NewDocumentCommand{\fpaddif}{O{} m O{} m }{%
  381. \IfNopText{#2}{#4}{#1#2#3#4}
  382. }
  383.  
  384. \NewDocumentCommand{\fppow}
  385. {
  386. s % optional *
  387. O{x}
  388. m % first mandatory argument
  389. m % second mandatory argument
  390. }{
  391. \setfpvar{numer}{round(1000*abs(#3)*(#3/#4)/abs(#3/#4))/1000}
  392. \setfpvar{denom}{round(1000*abs(#4))/1000}
  393. \def\xpow{#2^{\fpdiv*{\fv{numer}}{\fv{denom}}}}
  394. \def\xpowd{#2^{\fpdiv*{\fv{numer}}{1}}}
  395. %
  396. \IfBooleanTF{#1}
  397. {\xpow}%
  398. {\fpcompare{\fv{denom}=1}{\xpow}{\sqrt[\fphide{\fv{denom}}{2}]{\xpowd}}}
  399. }
  400.  
  401. \makeatletter
  402. \newcommand{\IfNopText}[3]{%
  403. \sbox0{#1}%
  404. \ifdim\wd0=0pt %
  405. {#2}% if #1 is empty
  406. \else%
  407. \ifdim0pt=\dimexpr\ht0+\dp0\relax
  408. {#2}% if #1 is empty
  409. \else
  410. {#3}% if #1 is not empty
  411. \fi
  412. \fi%
  413. }
  414. \makeatother
  415.  
  416.  
  417. \begin{document}
  418.  
  419. %==============================================================================%
  420. % ASSIGNMENT 01 %
  421. %==============================================================================%
  422.  
  423. \frontpageUiT
  424.  
  425. \UNItitlebox[norsk]
  426.  
  427. % Eksamen er individuell og skal besvares uten samarbeid med andre.
  428. % Alle hjelpemidler er tillatt (egne notater, pdfer fra forelesningene, lærebok,
  429. % internett etc). Alle eksamener som leveres i WISEflow blir automatisk sjekket
  430. % for plagiat. Det er ikke tillatt å kopiere medstudenter, nettressurser, kilder,
  431. % eller litteratur uten referanser.
  432.  
  433. \iSol{}{%
  434. Eksamen består av 20 delspørsmål, verdt 5 poeng hver, totalt 100 poeng. \\
  435. \textbf{Svar uten begrunnelse vil gi liten, til ingen uttelling}.%
  436. }
  437.  
  438. %==============================================================================%
  439. % PROBLEM 1 %
  440. %==============================================================================%
  441.  
  442. \input{TEK-0002-Problem-MixIntSeriesDiff.tex}
  443.  
  444. %==============================================================================%
  445. % PROBLEM 2 %
  446. %==============================================================================%
  447.  
  448. \input{TEK-0002-Problem-HeatOfVaporization-Goisteinum.tex}
  449.  
  450. %==============================================================================%
  451. % PROBLEM 3 %
  452. %==============================================================================%
  453.  
  454. \newpage
  455. \input{TEK-0002-Problem-Electricity-Series2Parallel.tex}
  456.  
  457.  
  458. %==============================================================================%
  459. % PROBLEM 4 %
  460. %==============================================================================%
  461.  
  462. \input{TEK-0002-Problem-Frequency-and-Prism.tex}
  463.  
  464.  
  465. %==============================================================================%
  466. % PROBLEM 5 %
  467. %==============================================================================%
  468.  
  469. \newpageLF
  470. \newpageNotLF
  471.  
  472. \input{TEK-0002-Problem-CenterOfMass-x2-sqrt-v2.tex}
  473.  
  474. %==============================================================================%
  475. % PROBLEM 2 %
  476. %==============================================================================%
  477.  
  478. % \begin{problem}
  479. % Ved jevn oppbremsing avtar farten $v$ lineært med tiden. Farten ved tiden
  480. % $t$ kan da skrives $v(t) = v_0 - at$, der $v_0$ er farten ved tiden $t=0$, og
  481. % $a$ er en konstant. Strekningen som tilbakelegges fra tiden $t=0$ og til
  482. % farten er null, vil vi kalle $B$ (bremselengden). Uttrykk $B$ som et bestemt
  483. % integral, og beregn integralet. (Har du regnet riktig vil du se at
  484. % brmselengden er proposjonal med kvadratet av farten $v_0$.)
  485. % \end{problem}
  486.  
  487. %==============================================================================%
  488. % PROBLEM 6 %
  489. %==============================================================================%
  490.  
  491. \newpageLF
  492.  
  493. \input{TEK-0002-Problem-PrimeDices.tex}
  494.  
  495.  
  496. %==============================================================================%
  497. % PROBLEM 7 %
  498. %==============================================================================%
  499.  
  500. \newpageNotLF
  501. \newpageLF
  502.  
  503. \input{TEK-0002-Problem-AmplitudeCosxSquared.tex}
  504.  
  505. \end{document}
  506.  
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