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doc476 e9eb877c-8ffc-403c-9547-dbb95d2d3700_OChem_and_Math_Test_worksheets-artifacted.pdf
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caption (11)
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formula (13)
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1 · TITLE
2 · TEXT
3 · LIST
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7 · TEXT
8
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10 · CAPTION
11 · FORMULA
12 · CAPTION
13 · FORMULA
14 · CAPTION
15 · FORMULA
16 · CAPTION
17 · FORMULA
18 · CAPTION
19 · FORMULA
20 · CAPTION
21 · FORMULA
22 · CAPTION
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24 · CAPTION
25 · FORMULA
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31 · FORMULA
Page 1 JSON
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"text": "1. Give the correct IUPAC name for the following organic compounds.",
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1 · TEXT
2 · TEXT
3 · HEADING
4 · FORMULA
5 · TEXT
6 · TEXT
7 · FORMULA
8 · FORMULA
9 · TEXT
10 · HEADING
11 · FORMULA
12 · FORMULA
13 · FOOTER
14 · FOOTER
Page 2 JSON
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"text": "Practice Test 4 Business Calculus",
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"text": "\\begin{aligned} &\\int x^{n}\\, dx = \\frac{x^{n+1}}{n+1} + C \\qquad \\int dx = x + C \\\\ &\\int e^{x}\\, dx = e^{x} + C \\\\ &\\int \\frac{1}{x}\\, dx = \\int x^{-1}\\, dx = \\ln|x| + C \\end{aligned}",
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"alt": "begin aligned & the integral of x to the power of n, dx equals x to the power of n plus 1 over n plus 1 plus C the integral of dx equals x plus C & the integral of e to the power of x, dx equals e to the power of x plus C & the integral of 1 over x, dx equals the integral of x to the power of minus 1, dx equals ln x plus C end aligned",
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"text": "MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.",
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"text": "\\begin{aligned} &1)\\ \\int(7x^{2}+1)\\,\\mathrm{d}x\\\\ &\\quad A)\\,14x+C\\qquad B)\\,x+C\\qquad \\textcircled{C}\\,\\frac{7}{3}x^{3}+x+C\\qquad D)\\,\\frac{7}{3}x^{3}+C\\\\ &=7\\,\\frac{x^{2+1}}{2+1}+\\ x+C\\ =\\ 7\\,\\frac{x^{3}}{3}+x+C\\\\[4pt] &2)\\ \\int 20\\,\\mathrm{d}x\\\\ &\\quad A)\\,10x^{2}\\qquad \\textcircled{B)}\\,20x+C\\qquad C)\\,0\\qquad D)\\,20+C\\\\ &=20x+C \\end{aligned}",
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"alt": "begin aligned &1 the integral of of 7 x squared plus 1, d x & A, 14 x plus C B, x plus C textcircled C, 7 over 3 x cubed plus x plus C D, 7 over 3 x cubed plus C & equals 7, frac x squared plus 1 2 plus 1 plus x plus C equals 7, x cubed over 3 plus x plus C 4 pt &2 the integral of 20, d x & A, 10 x squared textcircled B, 20 x plus C C, 0 D, 20 plus C & equals 20 x plus C end aligned",
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"text": "_{1)}\\underline{\\mathrm{C}}",
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"text": "2) $ B $",
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"text": "3) D",
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"text": "\\begin{aligned} &\\text{3)}~~\\int 7x^{-3}\\,\\mathrm{d}x \\qquad\\qquad \\text{3)}~\\underline{~\\text{D}~}\\\\ &\\text{A)}~x+7C \\qquad \\text{B)}~-21x+C \\qquad \\text{C)}~7x^{3} \\qquad \\textcircled{D}~-\\dfrac{7}{2x^{2}}+C\\\\ &=7\\,\\frac{x^{-3+1}}{-3+1}+C=7\\frac{x^{-2}}{-2}+C=-\\frac{7}{2}\\cdot\\frac{1}{x^{2}}+C \\end{aligned}",
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"latex": "\\begin{aligned} &\\text{3)}~~\\int 7x^{-3}\\,\\mathrm{d}x \\qquad\\qquad \\text{3)}~\\underline{~\\text{D}~}\\\\ &\\text{A)}~x+7C \\qquad \\text{B)}~-21x+C \\qquad \\text{C)}~7x^{3} \\qquad \\textcircled{D}~-\\dfrac{7}{2x^{2}}+C\\\\ &=7\\,\\frac{x^{-3+1}}{-3+1}+C=7\\frac{x^{-2}}{-2}+C=-\\frac{7}{2}\\cdot\\frac{1}{x^{2}}+C \\end{aligned}",
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"text": "\\begin{align*} &4)\\quad\\int 12x^{3}\\sqrt{x}\\,\\mathrm{d}x &&4)\\ \\underline{\\quad A\\quad}\\\\ &\\textcircled{A}\\ \\frac{8}{3}x^{9/2}+C \\qquad \\text{B)}\\ \\frac{11}{5}x^{9/2}+C \\qquad \\text{C)}\\ \\frac{24}{7}x^{9/2}+C \\qquad \\text{D)}\\ \\frac{2}{9}x^{9/2}+C\\\\ &=12\\int x^{3}\\cdot x^{\\frac{1}{2}}\\,\\mathrm{d}x=12\\int x^{3+\\frac{1}{2}}\\,\\mathrm{d}x=\\\\ &=12\\int x^{\\frac{7}{2}}\\,\\mathrm{d}x=12\\,\\frac{x^{\\frac{7}{2}+1}}{\\frac{7}{2}+1}+C\\\\ &=\\frac{12x^{\\frac{9}{2}}}{\\frac{9}{2}}+C=\\overset{4}{\\cancel{12}}\\cdot\\frac{2}{\\underset{3}{\\cancel{9}}}x^{\\frac{9}{2}}+C=\\frac{8}{3}x^{\\frac{9}{2}}+C \\end{align*}",
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"latex": "\\begin{align*} &4)\\quad\\int 12x^{3}\\sqrt{x}\\,\\mathrm{d}x &&4)\\ \\underline{\\quad A\\quad}\\\\ &\\textcircled{A}\\ \\frac{8}{3}x^{9/2}+C \\qquad \\text{B)}\\ \\frac{11}{5}x^{9/2}+C \\qquad \\text{C)}\\ \\frac{24}{7}x^{9/2}+C \\qquad \\text{D)}\\ \\frac{2}{9}x^{9/2}+C\\\\ &=12\\int x^{3}\\cdot x^{\\frac{1}{2}}\\,\\mathrm{d}x=12\\int x^{3+\\frac{1}{2}}\\,\\mathrm{d}x=\\\\ &=12\\int x^{\\frac{7}{2}}\\,\\mathrm{d}x=12\\,\\frac{x^{\\frac{7}{2}+1}}{\\frac{7}{2}+1}+C\\\\ &=\\frac{12x^{\\frac{9}{2}}}{\\frac{9}{2}}+C=\\overset{4}{\\cancel{12}}\\cdot\\frac{2}{\\underset{3}{\\cancel{9}}}x^{\\frac{9}{2}}+C=\\frac{8}{3}x^{\\frac{9}{2}}+C \\end{align*}",
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"alt": "begin align* &4 the integral of 12 x cubed the square root of x, d x &&4 underline A & textcircled A 8 over 3 x to the power of 9 over 2 plus C B 11 over 5 x to the power of 9 over 2 plus C C 24 over 7 x to the power of 9 over 2 plus C D 2 over 9 x to the power of 9 over 2 plus C & equals 12 the integral of x cubed times x to the power of 1 over 2, d x equals 12 the integral of x cubed plus 1 over 2, d x equals & equals 12 the integral of x to the power of 7 over 2, d x equals 12, x to the power of 7 over 2 plus 1 over 7 over 2 plus 1 plus C & equals 12 x to the power of 9 over 2 over 9 over 2 plus C equals overset 4 cancel 12 times frac 2 underset 3 cancel 9 x to the power of 9 over 2 plus C equals 8 over 3 x to the power of 9 over 2 plus C end align*",
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"text": "Business Calculus~ Nena Kabranski",
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