{ "\n": 57525, "!}": 58155, "##": 57681, "###": 57880, "####": 58227, "$$": 57531, "&-": 58121, "&0&": 58122, "&0\\\\": 58307, "&1": 57989, "&=&": 58476, "'s": 57959, "($": 58254, "(-": 57821, "(0)": 58157, "(0,": 58408, "(1+": 58036, "(1-": 57892, "(4": 58052, "(5": 58201, "(A": 57960, "(B": 58334, "(C": 58421, "(E": 58358, "(N": 58510, "(R": 58505, "(S": 58482, "(T": 58242, "(X": 58111, "(\\alpha": 58295, "(\\frac{": 57704, "(\\lambda": 58470, "(\\omega": 58218, "(\\theta": 58118, "(\\theta)": 58404, "(a": 57765, "(a)": 58193, "(b": 58062, "(b)": 58406, "(c": 58101, "(d": 58222, "(f": 58146, "(g": 58296, "(i": 57927, "(k": 57967, "(k)": 58412, "(m": 58180, "(n": 57843, "(n)": 58367, "(p": 58082, "(q": 58491, "(r": 58050, "(s": 57872, "(s)": 58171, "(t": 57659, "(t)": 57723, "(t)=": 58200, "(u": 58156, "(v": 58380, "(w": 58480, "(x": 57580, "(x)": 57670, "(x)=": 58017, "(x+": 58210, "(x,": 57955, "(x,y)": 58460, "(x-": 58127, "(y": 57996, "(y)": 58447, "(z": 57978, "(z)": 58239, "({\\bf": 58297, "))": 57835, ")+": 57698, ")-": 57786, ")=": 57574, ")=0": 58172, ")=\\frac{": 57903, ")\\": 57558, ")\\,": 57945, ")\\cdot": 58274, ")]": 58141, ")^2": 57972, ")^2}": 58448, ")^{": 57666, ")^{2}": 57874, ")^{2}}": 58346, ")}": 57566, ")}{": 57719, "+1)": 57962, "+1}": 57823, "+4": 58152, "+5": 58468, "+C": 58387, "+\\beta": 58497, "+\\frac{": 57699, "+\\frac{1}{": 58001, "+\\left(": 58504, "+\\sqrt{": 58492, "+a": 58205, "+b": 58091, "+c": 58221, "+i": 58350, "+x": 58102, "+{": 58012, ",\\": 57551, ",\\,": 57752, ",\\ldots,": 58235, ",\\quad": 58130, ",t)": 58220, "-1)": 57884, "-1}": 57664, "-1}{": 58442, "-2}": 58213, "-\\frac{": 57687, "-\\frac{1}{": 57997, "-\\infty": 58370, "-a": 58051, "-b": 58249, "-c": 58206, "-d": 58354, "-f": 58310, "-i": 58073, "-k": 58294, "-m": 58317, "-n": 58383, "-p": 58232, "-r": 58386, "-t": 58136, "-x": 57883, "-y": 58219, "-{": 58014, "/2}": 58110, "0&": 57816, "0&0&": 58418, "0,": 57716, "0.0": 58006, "0.1": 57941, "0.2": 58247, "0\\\\": 58060, "0}": 57564, "1": 57526, "1&": 57933, "1+": 57718, "1,": 57726, "1,2": 58467, "1-\\frac{": 58450, "1/2": 58166, "10^{": 58007, "10^{-": 58244, "10}": 58015, "11}": 58196, "12}": 58043, "13}": 58458, "15}": 58446, "16}": 58443, "1\\\\": 58237, "1}": 57540, "2&": 58289, "2,": 57894, "20}": 58414, "2\\pi": 57915, "2x": 57881, "2}": 57539, "2}}": 57595, "3,": 58149, "3x": 58191, "3}": 57578, "4\\pi": 58364, "4x": 58420, "4}": 57639, "5}": 57679, "6}": 57730, "7}": 57847, "8}": 57838, "9)": 58444, "9}": 57893, ":=": 58276, "": 57523, "": 57524, "": 57522, "=(": 57867, "=-": 57709, "=-\\frac{": 58181, "=0": 57661, "=0,": 58279, "=0.": 58076, "=0}^": 58202, "=0}^{": 58298, "=1}^": 57831, "=1}^{": 57877, "=4": 58211, "=A": 58502, "=\\dfrac{": 58290, "=\\frac{": 57575, "=\\frac{1}{": 57797, "=\\frac{1}{2": 58147, "=\\frac{1}{2}": 58269, "=\\frac{2": 58215, "=\\int": 57990, "=\\int_{": 58348, "=\\left(": 58113, "=\\left[": 58501, "=\\sqrt{": 58085, "=\\sum": 57963, "=\\sum_{": 58025, "=a": 58245, "=x": 58173, "={": 57888, ">0": 58381, "A_{": 57929, "A}": 57776, "B}": 57825, "C_{": 57954, "Cl": 58411, "C}": 57856, "D}": 58002, "E_{": 57973, "E}": 57896, "F_{": 58047, "F}": 57948, "Gamma": 58005, "G}": 58278, "H_{": 58107, "H}": 57895, "I_{": 58089, "I}": 58041, "J}": 58456, "K_{": 58208, "K}": 58179, "L}": 57866, "M_{": 58153, "M}": 57992, "Now": 58291, "N}": 57865, "O}": 58112, "P_{": 57928, "P}": 57912, "Q_{": 58344, "Q}": 58253, "R_{": 57969, "R}": 57783, "S_{": 58059, "S}": 57958, "T_{": 57922, "Then": 58270, "T}": 57762, "U}": 58449, "V_{": 57911, "V}": 57957, "W}": 58403, "X_{": 58075, "X}": 58055, "Y}": 58432, "Z}": 58248, "[1": 58243, "\\!": 57771, "\\,": 57549, "\\,,": 58252, "\\,.": 58302, "\\,\\,": 58013, "\\,\\,\\,": 58489, "\\,\\frac{": 58168, "\\,d": 57975, "\\:": 57932, "\\;": 57655, "\\;\\;": 58306, "\\Big": 57857, "\\Bigg": 58178, "\\Delta": 57732, "\\Gamma": 58020, "\\Lambda": 58192, "\\Omega": 58030, "\\Phi": 58120, "\\Psi": 58287, "\\Rightarrow": 58088, "\\Sigma": 58374, "\\\\": 57582, "\\alpha": 57631, "\\alpha}": 57905, "\\approx": 58263, "\\bar": 57839, "\\bar{": 57854, "\\begin{": 57665, "\\begin{array}{": 57755, "\\begin{array}{c": 57914, "\\begin{array}{cc": 58258, "\\begin{array}{c}": 58167, "\\begin{array}{l": 58109, "\\begin{array}{l}": 58303, "\\begin{bmatrix}": 58312, "\\beta": 57697, "\\beta}": 58105, "\\bf": 57736, "\\big": 57720, "\\bigg": 58103, "\\big{(}": 58373, "\\big{)}": 58369, "\\bold": 58115, "\\boldsymbol": 58162, "\\boldsymbol{": 58189, "\\cdot": 57599, "\\cdot\\": 57759, "\\cdots": 58064, "\\chi": 58163, "\\circ": 57942, "\\cos": 57680, "\\cos(": 58161, "\\cos\\theta": 58422, "\\delta": 57779, "\\delta_{": 58327, "\\dfrac": 57827, "\\dfrac{": 57837, "\\dot": 57819, "\\dot{": 57891, "\\ell": 58214, "\\end{array}": 57760, "\\end{bmatrix}": 58316, "\\epsilon": 57900, "\\equiv": 58216, "\\eta": 57988, "\\exp": 58198, "\\forall": 58437, "\\frac": 57536, "\\frac{": 57537, "\\frac{1}{": 57586, "\\frac{1}{2": 57725, "\\frac{1}{2}": 57781, "\\frac{1}{3}": 58429, "\\frac{1}{4}": 58486, "\\frac{1}{\\sqrt{": 58485, "\\frac{2": 57772, "\\frac{2}{": 58108, "\\frac{3}{": 58132, "\\frac{4}{": 58493, "\\frac{\\partial": 57789, "\\frac{\\pi": 58083, "\\frac{\\pi}{": 58175, "\\frac{\\sqrt{": 58452, "\\frac{d": 57794, "\\frac{n": 58336, "\\frac{x": 57995, "\\frac{x}{": 58477, "\\frac{{": 57986, "\\gamma": 57803, "\\gamma}": 58471, "\\geq": 58023, "\\hat": 57722, "\\hat{": 57739, "\\hbar": 58284, "\\hspace{": 58135, "\\hspace{0.17em}}": 58230, "\\in": 57569, "\\infty": 57702, "\\infty}": 57774, "\\int": 57648, "\\int\\limits": 58363, "\\int\\limits_{": 58426, "\\int_{": 57806, "\\int_{0}^{": 58195, "\\kappa": 58212, "\\lambda": 57689, "\\lambda}": 58160, "\\langle": 57965, "\\large": 58356, "\\ldots": 57956, "\\left": 57548, "\\left(": 57561, "\\left(\\begin{": 58288, "\\left(\\frac{": 57785, "\\left(x": 58016, "\\left(x\\right)": 58351, "\\left({": 57947, "\\left[": 57768, "\\left[\\begin{": 58293, "\\left\\{": 58067, "\\left|": 58072, "\\leq": 57770, "\\lim": 57812, "\\limits_{": 58096, "\\ln": 57936, "\\log": 57976, "\\mathbb": 57798, "\\mathbb{": 57807, "\\mathbb{R}": 58174, "\\mathbf": 57622, "\\mathbf{": 57623, "\\mathbf{x}": 58225, "\\mathcal": 57822, "\\mathfrak{": 58503, "\\mathrm": 57604, "\\mathrm{": 57605, "\\mathrm{d}": 58154, "\\mbox{": 57809, "\\mid": 58393, "\\mu": 57658, "\\mu_{": 58124, "\\mu}": 57926, "\\nabla": 57974, "\\neq": 58355, "\\nu": 57829, "\\nu}": 58065, "\\omega": 57694, "\\omega_{": 58081, "\\omega}": 58463, "\\operatorname{": 58271, "\\otimes": 58362, "\\over": 57758, "\\overline{": 57885, "\\overrightarrow": 58490, "\\partial": 57618, "\\phi": 57729, "\\phi}": 58391, "\\pi": 57620, "\\pi}": 57784, "\\pm": 58070, "\\prime": 57663, "\\psi": 57849, "\\qquad": 58024, "\\quad": 57749, "\\rangle": 57826, "\\rangle=": 58506, "\\rho": 57747, "\\rho_{": 58240, "\\rho}": 58343, "\\right": 57546, "\\right)": 57562, "\\right)+": 58255, "\\right)=": 57897, "\\right)\\left(": 58499, "\\right)^{2}": 58338, "\\right)}": 57845, "\\right.": 58228, "\\right\\}": 58209, "\\right]": 57775, "\\rightarrow": 58229, "\\right|": 58117, "\\rm": 57601, "\\rm{": 58277, "\\sigma": 57713, "\\sigma_{": 58084, "\\sigma}": 58322, "\\sim": 58337, "\\sin": 57677, "\\sin(": 58159, "\\sin\\theta": 58481, "\\sqrt": 57600, "\\sqrt{": 57613, "\\sqrt{2": 57980, "\\sqrt{2}": 58139, "\\sqrt{3}": 58264, "\\sqrt{\\frac{": 58321, "\\sum": 57660, "\\sum_{": 57690, "\\sum_{i": 58037, "\\sum_{i=1}^{": 58335, "\\sum_{j": 58464, "\\sum_{k": 58326, "\\sum_{n": 58280, "\\tag{": 57628, "\\tag{1": 57873, "\\tag{3": 58165, "\\tag{5": 58320, "\\tag{7": 58509, "\\tan": 58035, "\\tau": 57814, "\\tau}": 58410, "\\text": 57583, "\\text{": 57592, "\\theta": 57635, "\\theta)": 58100, "\\theta}": 57949, "\\tilde": 58028, "\\tilde{": 58040, "\\times": 57644, "\\times10": 58106, "\\times10^{": 58236, "\\to": 57734, "\\to0": 58435, "\\to\\infty": 58469, "\\varepsilon": 57913, "\\varphi": 57909, "\\vec": 57714, "\\vec{": 57763, "\\wedge": 58300, "\\xi": 57934, "\\zeta": 58431, "\\{": 57746, "\\|": 57917, "\\}": 57787, "],": 58438, "]=": 58140, "]{": 58398, "]}": 58056, "^2": 57585, "^2)": 58433, "^2+": 57938, "^2-": 58183, "^2=": 58465, "^2}": 57744, "^2}{": 58169, "^3": 57982, "^4": 58359, "^n": 58184, "^{": 57533, "^{*}": 57946, "^{+}": 58261, "^{-": 57641, "^{-1}": 57851, "^{-}": 58366, "^{0}": 58329, "^{1/": 58424, "^{1}": 58260, "^{2": 57552, "^{2}": 57554, "^{2})": 58197, "^{2}+": 57840, "^{2}-": 58045, "^{2}=": 58207, "^{2}}": 57676, "^{2}}{": 57924, "^{2}}}": 58388, "^{3}": 57887, "^{3}}": 58441, "^{4}": 58143, "^{T}": 58241, "^{\\circ}": 58177, "^{\\infty}": 57981, "^{\\prime": 57684, "^{\\prime}": 57693, "^{\\prime})": 58473, "^{\\prime}}": 58142, "^{\\rm": 58459, "^{i": 57998, "^{i}": 58397, "^{k}": 58379, "^{n}": 57916, "^{{}": 58498, "_0": 57899, "_1": 57790, "_1}": 58434, "_2": 57800, "_2}": 58415, "_3": 58301, "___": 58342, "_i": 57953, "_n": 58131, "_{": 57528, "_{0": 57626, "_{0}": 57637, "_{0})": 58347, "_{0}}": 58099, "_{1": 57577, "_{1}": 57591, "_{1})": 58259, "_{1}+": 58176, "_{1},": 58134, "_{1}=": 58275, "_{1}}": 57951, "_{2": 57596, "_{2}": 57612, "_{2})": 58257, "_{2}+": 58479, "_{2}=": 58372, "_{2}}": 57999, "_{3": 57805, "_{3}": 57842, "_{4}": 58203, "_{A": 58182, "_{A}": 58428, "_{B}": 58472, "_{\\alpha": 58137, "_{\\alpha}": 58405, "_{\\mathrm{": 58104, "_{\\mu}": 58313, "_{\\rm": 57701, "_{\\text{": 58265, "_{a}": 58151, "_{c": 58078, "_{c}": 58262, "_{f}": 58451, "_{i": 57597, "_{i=1}": 58133, "_{ij}": 58341, "_{i}": 57656, "_{i})": 58440, "_{i}^{": 58292, "_{i}}": 58223, "_{j": 57741, "_{j}": 57858, "_{k": 57721, "_{k}": 57864, "_{m": 57921, "_{m}": 58150, "_{n": 57662, "_{n}": 57750, "_{p": 58018, "_{p}": 58188, "_{r": 58074, "_{r}": 58286, "_{s}": 58186, "_{t": 57848, "_{t}": 58010, "_{x": 57834, "_{x}": 58086, "_{y}": 58400, "_{{": 57833, "_{{}_{": 57939, "a)": 57668, "a^2": 58199, "a^{2}": 57970, "a_{1}": 57985, "a_{2}": 58138, "a_{n}": 58478, "about": 58508, "ack": 58022, "align": 58507, "alpha": 57629, "also": 58246, "arc": 58349, "array": 57642, "arrow": 57710, "ass": 57828, "ature": 58352, "a}": 57570, "because": 58484, "both": 58353, "b}": 57792, "cause": 58323, "change": 58360, "const": 58033, "cos(": 58026, "c}": 57654, "def": 57919, "defined": 58318, "diff": 58004, "dition": 58158, "does": 58474, "dx": 57743, "dx=": 58461, "d}": 57673, "e^{": 57705, "e^{-": 57920, "e^{i": 58457, "ecause": 58382, "ency": 58494, "energy": 58266, "eq": 57579, "ess": 57757, "ext": 57576, "e}": 57603, "f(": 57731, "f(x": 57930, "f(x)": 58058, "f_{": 57940, "ference": 58365, "frac": 57535, "from": 57841, "function": 57818, "f}": 57832, "g_{": 58063, "gamma": 57795, "g}": 57889, "hich": 57844, "h}": 57918, "ined": 57984, "i}": 57568, "j}": 57691, "k}": 57671, "lect": 58044, "left": 57547, "length": 58339, "linear": 58361, "llows": 58399, "ln": 57862, "ly,": 58256, "l}": 57686, "matrix": 57706, "metric": 58376, "m}": 57653, "n't": 58333, "n+1": 58061, "n+1}": 58314, "n-1": 58066, "n-1}": 58281, "number": 57882, "n}": 57584, "n}}": 57966, "ode": 57977, "ond": 57853, "only": 58231, "ook": 58304, "oot": 58427, "opt": 58454, "ould": 57925, "ound": 58029, "own": 58071, "p}": 57715, "q}": 57944, "r^{2}": 58496, "rightarrow": 57868, "r}": 57650, "s,": 57669, "s.": 57737, "s:": 57796, "should": 58419, "sin(": 58009, "spect": 58273, "sqrt": 57598, "square": 58390, "subset": 58495, "such": 58251, "sym": 57968, "s}": 57683, "s}}": 58170, "t)": 57550, "t+": 58190, "these": 58392, "total": 58416, "t}": 57616, "t}}": 58123, "unc": 57769, "using": 58119, "u}": 57667, "v_{": 57993, "value": 57861, "vector": 58049, "very": 58328, "v}": 57852, "which": 57860, "will": 58054, "w}": 58053, "x)": 57634, "x+": 57740, "x+1": 58371, "x,y": 58164, "x-": 57777, "x-1": 58430, "x^": 57645, "x^2": 57898, "x^2+": 58439, "x^2}": 58409, "x^{": 57735, "x^{2}": 58031, "x_{1}": 58145, "x_{2}": 58324, "x_{i}": 58423, "x}": 57560, "x}+": 58315, "x}{": 57901, "x}}": 57910, "your": 58396, "y}": 57572, "z}": 57863, "{0}": 57608, "{10}": 58125, "{1}": 57544, "{2}": 57541, "{3}": 57607, "{A}": 57878, "{\\": 57529, "{\\bf": 57753, "{\\cal": 58097, "{\\frac{": 57692, "{\\frac{1}{": 58116, "{\\left(": 57907, "{\\left({": 58331, "{\\mathrm{": 57761, "{\\rm": 57610, "{\\rm{": 58455, "{\\text{": 57846, "{\\theta}": 58224, "{a}": 57756, "{b}": 57904, "{d}": 57801, "{p}": 57871, "{t}": 57820, "{x}": 57640, "{y}": 57875, "{z}": 58038, "{{": 57588, "{{{": 57943, "{}": 57675, "|^{2}": 58395, "|}": 58094, "}&": 57724, "}&{": 57991, "}(": 57553, "})": 57557, "})=": 57870, "}+": 57556, "}+\\frac{": 57830, "}+\\frac{1}{": 58272, "}+{": 58144, "}-": 57590, "}-\\frac{": 58003, "}-{": 58330, "}=": 57543, "}=-": 57950, "}=0": 57937, "}=1": 58000, "}=2": 58238, "}=\\frac{": 57652, "}=\\frac{1}{": 58079, "}[": 58090, "}\\": 57530, "}\\,": 57651, "}\\;": 58114, "}\\\\": 57751, "}\\cdot": 57799, "}\\end{array}": 58046, "}\\frac{": 57700, "}\\int_{": 58378, "}\\left(": 57708, "}\\left[": 58234, "}\\quad": 58299, "}\\right)": 57611, "}\\right)=": 58217, "}\\right)^{": 58093, "}\\right)}": 58027, "}\\right]": 57906, "}\\right|": 58413, "}\\times": 57923, "}]": 58032, "}^{": 57545, "}^{-1}": 58377, "}^{2}": 57685, "}^{\\infty}": 58019, "}_{": 57555, "}_{2}": 57952, "}_{\\rm": 58187, "}dx": 58488, "}{": 57534, "}{1": 57711, "}{1+": 58375, "}{1-": 58462, "}{2": 57594, "}{2}": 57638, "}{3": 57791, "}{3}": 57879, "}{4": 57813, "}{4}": 57935, "}{5}": 58250, "}{6}": 58309, "}{R": 58345, "}{\\partial": 57778, "}{\\sqrt{": 57979, "}{c}": 58042, "}{d": 57808, "}{dt}": 58233, "}{dx}": 58417, "}{m": 58368, "}{n": 58039, "}{n}": 58384, "}{r": 58128, "}{x}": 58148, "}|": 57869, "}}&{{": 58226, "}}+": 57902, "}}=": 57703, "}}=\\frac{": 58080, "}}\\,": 58077, "}}\\\\": 58282, "}}\\right)": 57931, "}}{": 57573, "}}{{": 57971, "}}}": 57643, "}}}}": 58069, "▁##": 57682, "▁$$": 57532, "▁$,": 57646, "▁$.": 57630, "▁&=": 58095, "▁(A": 57961, "▁(a": 57766, "▁(a)": 58194, "▁(b)": 58407, "▁**": 57855, "▁+\\": 57563, "▁0&": 57817, "▁0,": 57717, "▁0.": 57625, "▁1,": 57727, "▁=\\": 57542, "▁B}": 57824, "▁P(": 58011, "▁Solution": 58305, "▁Therefore": 58500, "▁\\": 57527, "▁\\$": 58402, "▁\\Delta": 57733, "▁\\Gamma": 58021, "▁\\Rightarrow": 58087, "▁\\\\": 57581, "▁\\alpha": 57632, "▁\\begin{bmatrix}": 58311, "▁\\beta": 57696, "▁\\delta": 57780, "▁\\dfrac{": 57836, "▁\\dot{": 57890, "▁\\forall": 58436, "▁\\frac{": 57538, "▁\\frac{1}{": 57587, "▁\\frac{1}{2}": 57782, "▁\\frac{2": 57773, "▁\\frac{\\partial": 57788, "▁\\frac{d": 57793, "▁\\gamma": 57802, "▁\\hat{": 57738, "▁\\int": 57647, "▁\\lambda": 57688, "▁\\langle": 57964, "▁\\large": 58357, "▁\\left[": 57767, "▁\\left\\{": 58068, "▁\\lim_{": 58092, "▁\\mathbf{": 57624, "▁\\mathrm{": 57606, "▁\\mbox{": 57810, "▁\\mu": 57657, "▁\\omega": 57695, "▁\\overline{": 57886, "▁\\partial": 57619, "▁\\phi": 57728, "▁\\pi": 57621, "▁\\psi": 57850, "▁\\rho": 57748, "▁\\rm": 57602, "▁\\sigma": 57712, "▁\\sin": 57678, "▁\\sqrt{": 57614, "▁\\tau": 57815, "▁\\text{": 57593, "▁\\theta": 57636, "▁\\varphi": 57908, "▁\\vec{": 57764, "▁\\{": 57745, "▁assum": 58483, "▁b)": 57987, "▁calculat": 58126, "▁calculate": 58308, "▁compl": 58325, "▁deno": 58319, "▁deriv": 58268, "▁distribution": 58487, "▁dx": 57742, "▁d}": 57672, "▁eas": 57876, "▁edge": 58185, "▁entr": 58332, "▁equal": 58129, "▁equation": 57811, "▁equations": 58385, "▁expression": 58425, "▁f(x)": 58057, "▁finite": 58466, "▁follows": 58453, "▁fraction": 58475, "▁hav": 57804, "▁is:": 58394, "▁i}": 57567, "▁length": 58340, "▁matrix": 57707, "▁operat": 57994, "▁partial": 57615, "▁probab": 58283, "▁probability": 58401, "▁r}": 57649, "▁simpl": 58204, "▁sl": 58008, "▁square": 58389, "▁triangle": 58445, "▁t}": 57617, "▁u=": 58285, "▁values": 58267, "▁vector": 58048, "▁wh": 57627, "▁x)": 57633, "▁x=": 57859, "▁x}": 57559, "▁y=": 58034, "▁y}": 57571, "▁{\\bf": 57754, "▁{\\cal": 58098, "▁{\\rm": 57609, "▁{{": 57589, "▁{}": 57674, "▁{}^{": 57983, "▁|": 57565 }