Function that takes a vector of text lines, x, and divides it in preamble and document.
Value
Returns a list with two character vectors:
- preamble
A character vector that includes every line of
xup the begin document command- document
A character vector that includes every line from the begin document command to the first end document command
Details
It ignores everything after the first end document command and it will throw and error if it finds more than one begin document command before that
See also
Other Structuring Document:
CompileDocument(),
FindStructure,
IsWellSectioned(),
StructureDocument()
Examples
file <- system.file(
"extdata",
"ExampleTexDocuments",
"exam_testing_jsonparser.tex",
package = "TexExamRandomizer"
)
x <- readLines(file)
DivideFile(x)
#> $preamble
#> [1] "% Studentds question collection"
#> [2] "%# Author Alejandro Gonzalez Recuenco and SKR students"
#> [3] "%# e-mail <alejandrogonzalezrecuenco@gmail.com>"
#> [4] ""
#> [5] "\\documentclass{exam}"
#> [6] "%SET-UP:"
#> [7] "\\usepackage{amsmath, physics, tikz, tcolorbox, graphicx}"
#> [8] ""
#> [9] ""
#> [10] "%! TexExamRandomizer = {\"noutput\":3, \"nquestions\": 13}"
#> [11] "%! TexExamRandomizer = {\"table\":\"../ExampleTables/TestClass.csv\"}"
#> [12] "%! TexExamRandomizer = {\"randominfo\": {\"switchnumber\":[\"even\", \"odd\"]}}"
#> [13] "%! TexExamRandomizer = {\"extrainfo\":{\"class\":\"Class\"}}"
#> [14] "%! TexExamRandomizer = {\"randominfo\": {\"randomnumber\":100000000}, \"extrainfo\":{\"rollnumber\":\"Roll Number\",\"nickname\":\"Nickname\"}, \"seed\":69504}"
#> [15] ""
#> [16] "\\newcommand{\\randomnumber}{3}"
#> [17] "\\newcommand{\\switchnumber}{hi}"
#> [18] "\\newcommand{\\class}{class}"
#> [19] "\\newcommand{\\rollnumber}{rollnumber}"
#> [20] "\\newcommand{\\nickname}{nickname}"
#> [21] "\\newcommand\\myversion{0}"
#> [22] "\\newcommand\\rseed{seed}"
#> [23] ""
#> [24] ""
#> [25] "% DOCUMENT STARTS HERE"
#>
#> $document
#> [1] "\\begin{document}"
#> [2] ""
#> [3] "\\author{\\class\\ --- \\nickname --- \\rollnumber}"
#> [4] "\\title{\\textsc{Exam collection} --- mini-exam, random \\randomnumber, switch \\switchnumber }"
#> [5] ""
#> [6] "\\date{seed:\\rseed, version:\\myversion}"
#> [7] "\\maketitle"
#> [8] ""
#> [9] ""
#> [10] "\\begin{questions}"
#> [11] ""
#> [12] "\\section{Word problems}"
#> [13] ""
#> [14] "\t\\question What is the mathematical definition of derivative."
#> [15] ""
#> [16] "\t\\begin{choices}"
#> [17] "\t\t\\choice $f'(x) = \\lim_{h\\to 0}$ $\\frac{f(x)-f(x)}{h+x}$"
#> [18] "\t\t\\choice $f'(x) = \\lim_{h\\to 0}$ $\\frac{f(x)-f(h)}{x}$"
#> [19] "\t\t\\choice $f'(x) = \\lim_{h\\to 0}$ $\\frac{f(x+h)+f(h)}{x}$"
#> [20] "\t\t\\CorrectChoice $f'(x) = \\lim_{h\\to 0}$ $\\frac{f(x+h)-f(x)}{h}$"
#> [21] "\t\\end{choices}"
#> [22] "\t\\question What is the derivative of the function $h(x) = \\frac{f(x)}{g(x)}$,"
#> [23] ""
#> [24] "\t\\begin{choices}"
#> [25] "\t\t\\choice $h'(x) = f'(g(x)) \\cdot g'(x).$"
#> [26] "\t\t\\choice $h'(x) = f'(x)g(x)-f(x)g'(x).$"
#> [27] "\t\t\\choice $h'(x) = f'(x)g(x)+f(x)g'(x).$"
#> [28] "\t\t\\CorrectChoice $h'(x) = \\frac{f(x)g'(x)-f'(x)g(x)}{(g(x))^2}.$"
#> [29] "\t\\end{choices}"
#> [30] ""
#> [31] "\t\\question Which one is the correct form of the chain rule ?"
#> [32] ""
#> [33] "\t\\begin{choices}"
#> [34] "\t\t\\choice $(f(g'))(x)=f'(g(x'))g'(x)$"
#> [35] "\t\t\\choice $(f(g'))'(x)=f'(g(x'))g'(x)$"
#> [36] "\t\t\\choice $(f(g))'(x)=f'(g'(x'))g'(x')$"
#> [37] "\t\t\\CorrectChoice $(f(g))'(x)=f'(g(x))g'(x)$"
#> [38] "\t\\end{choices}"
#> [39] ""
#> [40] "\t\\question Which of the following is NOT a type of discontinuity?"
#> [41] ""
#> [42] "\t\\begin{choices}"
#> [43] "\t\t\\choice Removable."
#> [44] "\t\t\\choice Infinite jump."
#> [45] "\t\t\\choice Finite jump."
#> [46] "\t\t\\CorrectChoice Endpoint."
#> [47] "\t\\end{choices}"
#> [48] ""
#> [49] "\t\\question What does a `Derivative' describe?"
#> [50] "\t\\begin{choices}"
#> [51] "\t\t\\choice It describes the instantaneous change of rate of the functions at $x$ axis."
#> [52] "\t\t\\choice It describes the instantaneous change of rate of the functions at $y$ axis."
#> [53] "\t\t\\choice It describes the instantaneous change of rate of the functions at some point."
#> [54] "\t\t\\CorrectChoice It describes the instantaneous change of rate of the functions at every point."
#> [55] "\t\\end{choices}"
#> [56] "\t\\question What is a tangent line to a curve at a point $x = a$?"
#> [57] ""
#> [58] "\t\\begin{choices}"
#> [59] "\t\t\\choice A line that crosses a curve once."
#> [60] "\t\t\\choice None of the other choices are correct."
#> [61] "\t\t\\choice A line that crosses a curve in two points."
#> [62] "\t\t\\CorrectChoice A line that has the same slope as the curve at the point $x = a$."
#> [63] "\t\\end{choices}"
#> [64] "\t\\question What type of graph is the derivative of $f(x)= 5x^3+6x^2+5x-1$ graph?"
#> [65] ""
#> [66] "\t\\begin{choices}"
#> [67] "\t\t\\choice Line."
#> [68] "\t\t\\choice Circle."
#> [69] "\t\t\\choice Hyperbola."
#> [70] "\t\t\\CorrectChoice Parabola."
#> [71] "\t\\end{choices}"
#> [72] "\t\\question The derivative of a function at a point $x = a$ tells us \\ldots"
#> [73] ""
#> [74] "\t\\begin{choices}"
#> [75] "\t\t\\choice The limit of the function"
#> [76] "\t\t\\choice The integral of the function."
#> [77] "\t\t\\choice The average rate of change."
#> [78] "\t\t\\CorrectChoice The slope of a tangent line of the graph at $x = a$."
#> [79] "\t\\end{choices}"
#> [80] ""
#> [81] "\\end{questions}"
#> [82] ""
#> [83] "\\begin{questions}"
#> [84] ""
#> [85] "\\section{Easy}"
#> [86] "\t\\question If $y=\\cos5x$ find $\\dv{y}{x}$."
#> [87] ""
#> [88] "\t\\begin{choices}"
#> [89] "\t\t\\choice $\\dv{y}{x} = 5\\cos5x$."
#> [90] "\t\t\\choice $\\dv{y}{x} = -2\\sin5x$."
#> [91] "\t\t\\choice $\\dv{y}{x} = 5\\cos2x$."
#> [92] "\t\t\\CorrectChoice $\\dv{y}{x} = -5\\sin5x$."
#> [93] "\t\\end{choices}"
#> [94] "\t\\question Given $y=2x^2-3x+5$, What is $\\dv[2]{y}{x}$"
#> [95] ""
#> [96] "\t\\begin{choices}"
#> [97] "\t\t\\choice $\\dv[2]{y}{x}=4x-3$"
#> [98] "\t\t\\choice $\\dv[2]{y}{x}=16x-12$"
#> [99] "\t\t\\choice $\\dv[2]{y}{x}=0$"
#> [100] "\t\t\\CorrectChoice $\\dv[2]{y}{x}=4$"
#> [101] "\t\\end{choices}"
#> [102] "\t\\question What is the derivative of $y=\\sin (2x + 5)$"
#> [103] ""
#> [104] "\t\\begin{choices}"
#> [105] "\t\t\\choice $ \\cos(2x+5)$"
#> [106] "\t\t\\CorrectChoice $ 2\\cos(2x+5)$"
#> [107] "\t\t\\choice $ 2\\cos(2x)+5$"
#> [108] "\t\t\\choice $ -2\\cos(2x-5)$"
#> [109] "\t\\end{choices}"
#> [110] ""
#> [111] ""
#> [112] "\t\\question If the functions $f(x)$ and $g(x)$ are continuous everywhere then, what can we say about the function $h(x) = \\frac{f(x)}{g(x)}$:"
#> [113] ""
#> [114] "\t\\begin{choices}"
#> [115] "\t\t\\CorrectChoice $\\frac{f(x)}{g(x)}$ is also continuous everywhere except at the zeros of $g(x)$."
#> [116] "\t\t\\choice $h(x) = \\frac{f(x)}{g(x)}$ is also continuous everywhere."
#> [117] "\t\t\\choice $h(x)$ will never cross the x axis."
#> [118] "\t\t\\choice More information is needed to answer this question."
#> [119] "\t\\end{choices}"
#> [120] ""
#> [121] ""
#> [122] "\t\\question Find the value of $\\lim_{x\\to 2}\\frac{x-1}{x^2-x-1}$"
#> [123] ""
#> [124] "\t\\begin{choices}"
#> [125] "\t\t\\choice $0$."
#> [126] "\t\t\\CorrectChoice $1$."
#> [127] "\t\t\\choice $\\infty$."
#> [128] "\t\t\\choice Not possible."
#> [129] "\t\\end{choices}"
#> [130] ""
#> [131] "\t\\question What is the derivative of $f(x)= 3x^4+2x^3-3x-2$"
#> [132] "\t\\begin{choices}"
#> [133] "\t\t\\choice $f'(x)= 3x^7+2x^6-3x^3-2$."
#> [134] "\t\t\\choice $f'(x)= 12x^3+6x^2-5$."
#> [135] "\t\t\\choice $f'(x)= 7x^4+5x^3-4x-2$."
#> [136] "\t\t\\CorrectChoice $f'(x)= 12x^3+6x^2-3$."
#> [137] "\t\\end{choices}"
#> [138] "\t\\question What is the derivative of $(x^{2} + 3)(5 x + 2)$ ?"
#> [139] ""
#> [140] "\t\\begin{choices}"
#> [141] "\t\t\\choice $15 x^{2} + 19 x$"
#> [142] "\t\t\\choice $50 x^{2} + 60 x$"
#> [143] "\t\t\\choice $2 x + 5$"
#> [144] "\t\t\\CorrectChoice $15 x^{2} + 4 x + 15$"
#> [145] "\t\\end{choices}"
#> [146] "\t\\question When $f'(x) = 0$ what happens?"
#> [147] ""
#> [148] "\t\\begin{choices}"
#> [149] "\t\t\\choice $f''(x) = 1$"
#> [150] "\t\t\\choice $f''(x) = 0 $"
#> [151] "\t\t\\CorrectChoice The point is a critical point"
#> [152] "\t\t\\choice Local maximum or minimum or an inflection point."
#> [153] "\t\\end{choices}"
#> [154] "\t\\question What is the derivative of $f(x) = (2x+8)^2$"
#> [155] ""
#> [156] "\t\\begin{choices}"
#> [157] "\t\t\\choice $32$"
#> [158] "\t\t\\choice $3x+32$"
#> [159] "\t\t\\choice $4x+32$"
#> [160] "\t\t\\CorrectChoice $8x+32$"
#> [161] "\t\\end{choices}"
#> [162] ""
#> [163] "\t\\question If $f(x) =\\sqrt{x^3 - 4x}$, calculate when $f(x)=0 $"
#> [164] ""
#> [165] "\t\\begin{choices}"
#> [166] "\t\t\\choice $x = 0,\\,1,\\,{-1}$"
#> [167] "\t\t\\choice $x= 0, $"
#> [168] "\t\t\\choice $x= 0,\\,2 $"
#> [169] "\t\t\\CorrectChoice$ x= 0,\\,2,\\,{-2} $"
#> [170] "\t\\end{choices}"
#> [171] "\t\\question Given $f(x) = \\frac{x^3-4}{2x+2}$, then $\\lim_{x\\to 4} f(x) = \\ldots$"
#> [172] ""
#> [173] "\t\\begin{choices}"
#> [174] "\t\t\\choice $\\ldots3.$"
#> [175] "\t\t\\choice $\\ldots4.$"
#> [176] "\t\t\\choice $\\ldots5.$"
#> [177] "\t\t\\CorrectChoice $\\ldots6.$"
#> [178] "\t\\end{choices}"
#> [179] "\t\\question Suppose $f(x) = x^2 + 3$ and $g(x) = x - 2$. Which of the following is $(f-g)(x)$?"
#> [180] ""
#> [181] "\t\\begin{choices}"
#> [182] "\t\t\\choice $(f-g)(x)=x^2 - x +1$"
#> [183] " \t\\choice $(f-g)(x)=x^3 + 2x^2 + 3x -2$"
#> [184] "\t\t\\choice $(f-g)(x)=x^2 - 4x + 7$"
#> [185] "\t\t\\CorrectChoice $(f-g)(x)=x^2 - x + 5$"
#> [186] "\t\\end{choices}"
#> [187] ""
#> [188] "\t\\question Given the functions $f(x) = x^4+3$ and $g(x) = \\sqrt{x}$, find the value of $(f\\circ g)'(x)\\ldots$"
#> [189] ""
#> [190] "\t\\begin{choices}"
#> [191] "\t\t\\choice $(f\\circ g)'(x) = x$"
#> [192] "\t\t\\CorrectChoice $(f\\circ g)'(x) = 2x$"
#> [193] "\t\t\\choice $(f\\circ g)'(x) = 3x$"
#> [194] "\t\t\\choice $(f\\circ g)'(x) = 4x$"
#> [195] "\t\\end{choices}"
#> [196] "\t\\question Which one is the correct form of the product rule?"
#> [197] ""
#> [198] "\t\\begin{choices}"
#> [199] "\t\t\\choice $(f(x)\\cdot g(x))' = f'(x)g'(x)+f'(x)g'(x)$"
#> [200] "\t\t\\choice $(f(x)\\cdot g(x))' = f'(x)g'(x)+f(x)g(x)$"
#> [201] "\t\t\\choice $(f(x)\\cdot g(x))' = f(x)g'(x)+f(x)g'(x)$"
#> [202] "\t\t\\CorrectChoice $(f(x)\\cdot g(x))' = f'(x)g(x) + f(x)g'(x)$"
#> [203] "\t\\end{choices}"
#> [204] ""
#> [205] "\t\\question What is the derivative of $f(x) = \\sqrt{4x+5}$"
#> [206] ""
#> [207] "\t\\begin{choices}"
#> [208] "\t\t\\choice $2\\sqrt{x+5}$."
#> [209] "\t\t\\choice $8$."
#> [210] "\t\t\\choice $\\frac{\\sqrt{4x+5}}{2}$."
#> [211] "\t\t\\CorrectChoice $\\frac{2}{\\sqrt{4x+5}}$."
#> [212] "\t\\end{choices}"
#> [213] "\t\\question Calculate the derivative of $f(x) = 2x^2+3$"
#> [214] ""
#> [215] "\t\\begin{choices}"
#> [216] "\t\t\\CorrectChoice $f'(x) = 4x$"
#> [217] "\t\t\\choice $f'(x) = 2x$"
#> [218] "\t\t\\choice $f'(x) = 5x$"
#> [219] "\t\t\\choice $f'(x) = 6x$"
#> [220] "\t\\end{choices}"
#> [221] "\t\\question Calculate the derivative of $y=\\sin(3x{^2}+1)$"
#> [222] ""
#> [223] "\t\\begin{choices}"
#> [224] "\t\t\\choice $\\dv{y}{x} = \\sin(3x{^2}+1)$"
#> [225] "\t\t\\choice $\\dv{y}{x} = \\cos(3x{^2}+1)$"
#> [226] " \\choice $\\dv{y}{x} = 6x\\sin(3x{^2}+1)$"
#> [227] "\t\t\\CorrectChoice $\\dv{y}{x} = 6x \\cos(3x{^2}+1)$"
#> [228] "\t\\end{choices}"
#> [229] "\t\\question Find the derivative of $f(x) = \\sqrt[6]{4x+4}$"
#> [230] ""
#> [231] "\t\\begin{choices}"
#> [232] "\t\t\\choice $f'(x) = 4 (4x+4)^{-1/3} $"
#> [233] "\t\t\\choice $f'(x) = \\frac{4x }{6 \\sqrt[3]{4x+4}}$"
#> [234] "\t\t\\choice $f'(x) = \\frac{4 x + 4}{6 \\sqrt[6]{(4x + 4)^{5}}} $"
#> [235] "\t\t\\CorrectChoice $f'(x) = \\frac{4}{6 \\sqrt[6]{(4x + 4)^{5}}}$"
#> [236] "\t\\end{choices}"
#> [237] ""
#> [238] "\\end{questions}"
#> [239] ""
#> [240] ""
#> [241] ""
#> [242] ""
#> [243] "\\begin{questions}"
#> [244] ""
#> [245] "\\section{Medium}"
#> [246] "\t\\question What is the derivative of f(x)=$(1-6x^2)^4$"
#> [247] "\t\\begin{choices}"
#> [248] "\t\t\\choice $4(1-6x^2)^3$"
#> [249] "\t\t\\choice $4x(1-6x^2)^3$"
#> [250] "\t\t\\choice $48x(1-6x^2)^3$"
#> [251] "\t\t\\CorrectChoice $-48x(1-6x^2)^3 y$"
#> [252] "\t\\end{choices}"
#> [253] ""
#> [254] "\t\\question Find the slope of the tangent line of the curve $y = \\frac{1}{x}$ at the point $(3,\\frac13)$"
#> [255] ""
#> [256] "\t\\begin{choices}"
#> [257] "\t\t\\choice $\\frac{1}{3}$"
#> [258] "\t\t\\choice $\\frac{-1}{3}$"
#> [259] "\t\t\\choice $\\frac{1}{9}$"
#> [260] "\t\t\\CorrectChoice $\\frac{-1}{9}$"
#> [261] "\t\\end{choices}"
#> [262] ""
#> [263] "\t\\question Calculate the following limit: $\\lim_{x \\to -2} = \\frac{x^3+8}{x+2}\\ $"
#> [264] ""
#> [265] "\t\\begin{choices}"
#> [266] "\t\t\\choice $\\infty$."
#> [267] "\t\t\\choice $4$."
#> [268] "\t\t\\choice $1$."
#> [269] "\t\t\\CorrectChoice $12$."
#> [270] "\t\\end{choices}"
#> [271] "\t\\question Is this function continuous or discontinuous? $f(x) = \\frac{x+8}{x-4}$"
#> [272] ""
#> [273] "\t\\begin{choices}"
#> [274] "\t\t\\choice Continuous."
#> [275] "\t\t\\choice Discontinuous, contains a removable discontinuities."
#> [276] "\t\t\\choice No other answer is correct."
#> [277] "\t\t\\CorrectChoice Discontinuous, contains a jump discontinuities."
#> [278] "\t\\end{choices}"
#> [279] ""
#> [280] "\t\\question $\\displaystyle \\lim_{x\\to 4}{x^{2} + 2 x - 4}$ ?"
#> [281] ""
#> [282] "\t\\begin{choices}"
#> [283] "\t\t\\choice 14"
#> [284] "\t\t\\choice 16"
#> [285] "\t\t\\choice 18"
#> [286] "\t\t\\CorrectChoice 20"
#> [287] "\t\\end{choices}"
#> [288] ""
#> [289] "\t\\question What is the name of the functions $\\frac1{\\cos x}$ ?"
#> [290] "\t\\begin{choices}"
#> [291] "\t\t\\choice $\\csc x$"
#> [292] "\t\t\\choice $\\cot x$"
#> [293] "\t\t\\choice $\\tan x$"
#> [294] "\t\t\\CorrectChoice $\\sec x$"
#> [295] "\t\\end{choices}"
#> [296] ""
#> [297] "\t\\question Find the value of $\\displaystyle \\lim_{x \\to 6} \\frac{x^2 -36}{x^3 -216}$"
#> [298] ""
#> [299] "\t\\begin{choices}"
#> [300] "\t\t\\choice $\\frac{1}{6}$"
#> [301] "\t\t\\CorrectChoice $\\frac{1}{9}$"
#> [302] "\t\t\\choice $\\frac{1}{12}$"
#> [303] "\t\t\\choice $\\frac{1}{15}$"
#> [304] "\t\\end{choices}"
#> [305] "\t\\question What is the function $f$ whose derivative is $f'(x)=x^5 +30$"
#> [306] ""
#> [307] " \\begin{choices}"
#> [308] "\t\t\\choice $f(x) = 5x^4 +30x$"
#> [309] "\t\t\\choice $f(x) = 5x^4$"
#> [310] "\t\t\\choice $f(x) = x^6 +30x$"
#> [311] "\t\t\\CorrectChoice $f(x) = \\frac{x^6}{6} +30x$"
#> [312] "\t\\end{choices}"
#> [313] "\t\\question Find the derivative of $f(x) = \\frac{x-1}{x+1}$"
#> [314] ""
#> [315] "\t\\begin{choices}"
#> [316] "\t\t\\choice $f'(x) = \\frac{-2}{(x+1)^2}$"
#> [317] "\t\t\\choice $f'(x) = \\frac{2}{(x-1)^2}$"
#> [318] "\t\t\\choice $f'(x) = \\frac{-2}{(x-1)^2}$"
#> [319] "\t\t\\CorrectChoice $f'(x) = \\frac{2}{(x+1)^2}$"
#> [320] "\t\\end{choices}"
#> [321] ""
#> [322] "\\end{questions}"
#> [323] ""
#> [324] ""
#> [325] ""
#> [326] ""
#> [327] "\\begin{questions}"
#> [328] ""
#> [329] "\\section{Hard}"
#> [330] "\t\\question Calculate $\\lim_{x\\to 1}\\frac{\\sin (2x^2-2)}{x^2-1}$. (Hint: L'H\\^opital rule)"
#> [331] ""
#> [332] "\t\\begin{choices}"
#> [333] "\t\t\\choice $1$"
#> [334] "\t\t\\choice $-1$"
#> [335] "\t\t\\choice The limit does not exist."
#> [336] "\t\t\\CorrectChoice $2$"
#> [337] "\t\\end{choices}"
#> [338] "\t\\question What is the local minimum of $x^3-2x^2$ in the range where $-1<x<1$?"
#> [339] ""
#> [340] "\t\\begin{choices}"
#> [341] "\t\t\\choice $x=0$"
#> [342] "\t\t\\choice $x=-1$"
#> [343] "\t\t\\choice There is no local minimum in that range."
#> [344] "\t\t\\CorrectChoice $x=\\frac43$"
#> [345] "\t\\end{choices}"
#> [346] "\t\\question What is the derivative of $f(x) = 2x \\sin x + 2 \\cos x - x^{2}\\cos x.$"
#> [347] ""
#> [348] "\t\\begin{choices}"
#> [349] "\t\t\\choice $f'(x) = x^{2} \\sin x + 2 x \\cos x -2\\sin x$."
#> [350] "\t\t\\choice $f'(x) = x^{2}\\cos x$."
#> [351] "\t\t\\choice $f'(x) = 2x\\cos x$."
#> [352] "\t\t\\CorrectChoice $f'(x) = x^{2}\\sin x$."
#> [353] "\t\\end{choices}"
#> [354] ""
#> [355] "\t\\question What is value of the $\\displaystyle \\lim_{h \\to 0} \\frac{f(x+h) -f(x)}{h}$ tells about the function?"
#> [356] ""
#> [357] "\t\\begin{choices}"
#> [358] "\t\t\\choice\\label{choice:der1} The Slope of the graph."
#> [359] "\t\t\\choice\\label{choice:der2} The critical point of the function , when the value of the limit is 0."
#> [360] "\t\t\\CorrectChoice Both options, \\ref{choice:der1} and \\ref{choice:der2}, are correct."
#> [361] "\t\t\\choice None of the above."
#> [362] "\t\\end{choices}"
#> [363] ""
#> [364] "\t\\question What is the derivative of $f(x) = \\arctan(2x)$ ?"
#> [365] ""
#> [366] "\t\\begin{choices}"
#> [367] "\t\t\\choice $\\frac{2}{1 + x^{2}}$"
#> [368] "\t\t\\choice $\\frac{2}{2 + x^{2}}$"
#> [369] "\t\t\\choice $\\frac{2}{2 + 4x^{2}}$"
#> [370] "\t\t\\CorrectChoice $\\frac{2}{1 + 4x^{2}}$"
#> [371] "\t\\end{choices}"
#> [372] "\t\\question Find the derivatives of f(x) = $\\sin^6(x^4)$"
#> [373] ""
#> [374] "\t\\begin{choices}"
#> [375] "\t\t\\choice $6\\sin^{5}(x^4)$"
#> [376] "\t\t\\choice $24 x^{3}\\sin(x^3) \\sin(x^4)$"
#> [377] "\t\t\\choice $24\\sin(x^4) \\cos(x^3)$"
#> [378] "\t\t\\CorrectChoice $24 x^{3} \\sin^{5}(x^4) \\cos(x^4) $"
#> [379] "\t\\end{choices}"
#> [380] "\t\\question Find the derivative of $f(x)$ = $\\sqrt{x^2+3x}$."
#> [381] ""
#> [382] "\t\\begin{choices}"
#> [383] "\t\t\\choice $f'(x) = \\frac{1}{2}\\sqrt{2x+3}$."
#> [384] "\t\t\\choice $f'(x) = \\frac{1}{x^2+3x}(2x+3)$."
#> [385] "\t\t\\choice $f'(x) = \\frac{-1}{2 \\sqrt{2x + 3}}$."
#> [386] "\t\t\\CorrectChoice $f'(x) = \\frac{2x + 3}{2 \\sqrt{2x + 3}}$."
#> [387] "\t\\end{choices}"
#> [388] ""
#> [389] ""
#> [390] "\\end{questions}"
#> [391] ""
#> [392] ""
#> [393] "\\begin{questions}"
#> [394] "\\section{Graphic problems}"
#> [395] "\t\\question"
#> [396] "\tFrom the following graph find $\\lim_{x \\to -2 } f(x)$"
#> [397] "\t\\par\\nopagebreak"
#> [398] "\t\\includegraphics[width = 6cm]{limgraph.jpg}"
#> [399] ""
#> [400] "\t\\begin{choices}"
#> [401] "\t\t\\choice $0$."
#> [402] "\t\t\\choice $5$."
#> [403] "\t\t\\choice $4$."
#> [404] "\t\t\\CorrectChoice undefined."
#> [405] "\t\\end{choices}"
#> [406] ""
#> [407] "\\end{questions}"
#> [408] ""
#> [409] ""
#> [410] "\\begin{questions}"
#> [411] "\\section{Bonus, integration}"
#> [412] "\t\\question Find the area of the graph between f(x) = $x^4$ and f(x) = $(x-6)^4$"
#> [413] ""
#> [414] "\t\\begin{choices}"
#> [415] "\t\t\\choice $\\frac{243}{5}$"
#> [416] "\t\t\\choice $\\frac{243}{10}$"
#> [417] "\t\t\\choice $\\frac{486}{10}$"
#> [418] "\t\t\\CorrectChoice $\\frac{486}{5}$"
#> [419] "\t\\end{choices}"
#> [420] "\t\\question Find the integral of $ 4x^3+3x^2 $"
#> [421] ""
#> [422] "\t\\begin{choices}"
#> [423] "\t\t\\choice $12x^2 + 6x$"
#> [424] "\t\t\\choice $4x^2 + 3x$"
#> [425] "\t\t\\choice $4x^4 + 3x^3 + c$"
#> [426] "\t\t\\CorrectChoice $x^4 + x^3 +c$"
#> [427] "\t\\end{choices}"
#> [428] "\t\\question What is the area under the graph $y = x^3$, the line $y = 0$ and the lines $x=0$ and $x=2$?"
#> [429] ""
#> [430] "\t\\begin{choices}"
#> [431] "\t\t\\choice 8"
#> [432] "\t\t\\choice 16"
#> [433] "\t\t\\choice 24"
#> [434] "\t\t\\CorrectChoice 4"
#> [435] "\t\\end{choices}"
#> [436] "\t\\question Which of these processes are used to calculate the area under a curve?"
#> [437] "\t\\begin{choices}"
#> [438] "\t\t\\choice First derivative"
#> [439] "\t\t\\choice Product rule"
#> [440] "\t\t\\choice Second derivative"
#> [441] "\t\t\\CorrectChoice Integral"
#> [442] "\t\\end{choices}"
#> [443] ""
#> [444] ""
#> [445] ""
#> [446] ""
#> [447] "\\end{questions}"
#> [448] ""
#> [449] "\\end{document}"
#>