{"classes":[{"calculus":[{ "limits":[{"question": "\\lim_{x \\to \\frac{\\pi}{4}}\\left(- \\frac{12 \\cot{\\left(x \\right)}}{5 - 3 x}\\right)", "options": ["1", "\\infty", "\\frac{48}{-20 + 3 \\pi}",  "\\frac{24}{2\\pi}"], "answer": "C"},{"question":"\\lim_{x \\to 0}\\left(- \\frac{9 \\cos{\\left(x \\right)}}{3 x + 3}\\right)", "options":["-3","2","\\infty","0"], "answer": "A"}, {"question": "\\lim_{x \\to -2}\\left(- \\frac{12}{x \\left(4 x - 1\\right)}\\right)", "options" : ["3" , "- \\frac{2}{3}", "1", "\\infty"], "answer": "B"}, {"question": "\\lim_{x \\to -1}\\left(\\frac{9}{x^{5} \\left(- 3 x - 5\\right)}\\right)", "options" :["\\frac{3}{4}", "\\frac{9}{2}", "\\infty", "-1"], "answer":"B"}, {"question": "\\lim_{x \\to \\frac{\\pi}{2}}\\left(\\frac{10 \\sin{\\left(x \\right)}}{5 x - 2}\\right)", "options": ["\\frac{20\\pi}{3 + \\pi}", "\\frac{20}{-4 + 5 \\pi}", "\\frac{30}{4-8\\pi}", "\\infty"], "answer": "B"}, {"question": "\\lim_{x \\to \\frac{\\pi}{3}}\\left(\\frac{6 \\tan{\\left(x \\right)}}{2 x - 1}\\right)", "options": ["4", " \\frac{9\\sqrt{2}}{\\pi}", "\\frac{2\\sqrt{5}}{3}", "\\frac{18 \\sqrt{3}}{-3 + 2 \\pi}"], "answer": "D"}, {"question": "\\lim_{x \\to 3}\\left(- \\frac{12 x^{3}}{3 - 4 x}\\right)", "options": ["10", "1", "36", "0"], "answer": "C"}, {"question": "\\lim_{x \\to - \\frac{\\pi}{2}}\\left(\\frac{12 \\cot{\\left(x \\right)}}{4 x + 1}\\right)", "options": ["1", "0", "\\infty", "-1"], "answer": "B"}, {"question": "\\lim_{x \\to - \\frac{\\pi}{2}}\\left(\\frac{20 \\cos{\\left(x \\right)}}{- 5 x - 2}\\right)", "options": ["0", "1", "-1", "\\frac{1}{2}"], "answer": "A"}, {"question": "\\lim_{x \\to - \\pi^+}\\left(\\frac{10 \\tan{\\left(x \\right)}}{- 5 x - 3}\\right)", "options": ["\\infty", "1", "\\sqrt{3}", "0"], "answer": "D"}, {"question": "\\lim_{x \\to 1^+}\\left(\\frac{25 x}{- 3 x - 2}\\right)", "options": ["-5", "25", "-25", "5"], "answer": "A"}, {"question": "\\lim_{x \\to \\frac{\\pi}{2}^+}\\left(- \\frac{4 \\tan{\\left(x \\right)}}{3 - x}\\right)", "options": ["0", "1", "\\infty", "-1"], "answer": "C"}, {"question": "\\lim_{x \\to - \\pi^+}\\left(- \\frac{2 \\sin{\\left(x \\right)}}{x - 3}\\right)", "options": ["-1", "0", "\\frac{1}{2}", "1"], "answer" : "B"}, {"question": "\\lim_{x \\to - \\pi^+}\\left(- \\frac{4 \\cot{\\left(x \\right)}}{- 4 x - 2}\\right)", "options": ["\\infty", "1", "0", "-\\infty"], "answer": "D"}, {"question": "\\lim_{x \\to - \\pi^+}\\left(\\frac{2 \\cot{\\left(x \\right)}}{x - 3}\\right)", "options" : ["0", "1" , "-\\infty", "\\infty"], "answer": "C"}, {"question": "\\lim_{x \\to 1^+}\\left(- \\frac{20}{x^{2} \\left(4 x - 2\\right)}\\right)", "options": ["-\\frac{10}{3}", "-10", "10", "\\frac{10}{3}"], "answer": "B"}, {"question": "\\lim_{x \\to -1^+}\\left(\\frac{9}{x \\left(5 x + 1\\right)}\\right)", "options": ["\\frac{3}{2}", "\\frac{9}{4}", "\\frac{9}{5}", "-\\frac{9}{5}"], "answer": "B"}, {"question": "\\lim_{x \\to 0^-}\\left(\\frac{4 \\cos{\\left(x \\right)}}{2 x - 1}\\right)", "options": ["-4", "0", "4", "-1"], "answer": "A"}, {"question": "\\lim_{x \\to 3^-}\\left(\\frac{x^{3}}{5 - 2 x}\\right)", "options": ["-27", "27", "9", "-9"], "answer": "A"}, {"question": "\\lim_{x \\to 0^-}\\left(- \\frac{3 x^{4}}{4 - x}\\right)", "options": ["1", "\\infty", "0", "-1"], "answer": "C"}], "continuity": [{"question": " \\lim_{x \\to \\frac{\\pi}{3}}\\left(- \\frac{8 \\csc{\\left(x \\right)}}{2 - 4 x}\\right)" ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{20 \\tan{\\left(x \\right)}}{4 x + 3}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 3}\\left(5 x^{4}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"}, {"question": " \\lim_{x \\to 3}\\left(- \\frac{15}{x^{5} \\left(- 5 x - 3\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -3}\\left(\\frac{4}{x^{3} \\left(x - 3\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(\\frac{4 \\sin{\\left(x \\right)}}{x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -4}\\left(\\frac{25}{x^{4} \\left(5 x + 1\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{4 \\sin{\\left(x \\right)}}{4 x - 2}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 3}\\left(\\frac{20}{x^{4} \\left(1 - 5 x\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -4}\\left(\\frac{15}{x^{4} \\left(- 5 x - 5\\right)}\\right)" ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -2}\\left(\\frac{20 x^{5}}{4 x - 5}\\right)" ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -2}\\left(- \\frac{16}{x^{2} \\left(4 - 2 x\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to \\pi}\\left(- \\frac{4 \\csc{\\left(x \\right)}}{- 4 x - 1}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\frac{\\pi}{3}}\\left(\\frac{8 \\tan{\\left(x \\right)}}{4 x - 2}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{3}}\\left(\\frac{4 \\sin{\\left(x \\right)}}{5 - 2 x}\\right)" ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 0}\\left(\\frac{2 \\cos{\\left(x \\right)}}{- x - 5}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{4}}\\left(\\frac{4 \\cos{\\left(x \\right)}}{2 x + 5}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -3}\\left(\\frac{6 x^{2}}{2 x + 2}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -3}\\left(\\frac{16}{x^{3} \\left(- 4 x - 1\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to \\frac{\\pi}{3}}\\left(\\frac{16 \\tan{\\left(x \\right)}}{3 - 4 x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -1}\\left(- \\frac{5}{x^{2} \\left(- x - 2\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{20 \\tan{\\left(x \\right)}}{2 - 4 x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -4}\\left(\\frac{4}{x^{4} \\left(- 4 x - 3\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 3}\\left(- \\frac{4}{x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -3}\\left(\\frac{25}{x^{3} \\left(1 - 4 x\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -4}\\left(- \\frac{1}{5 x^{4}}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{3 \\cot{\\left(x \\right)}}{- x - 1}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to \\pi}\\left(\\frac{20 \\sin{\\left(x \\right)}}{- 5 x - 1}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{4}}\\left(- \\frac{4 \\sec{\\left(x \\right)}}{- 2 x - 3}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 0}\\left(\\frac{4 \\tan{\\left(x \\right)}}{4 - x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{10 \\tan{\\left(x \\right)}}{5 x - 1}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 1}\\left(3 x^{2}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{2 x}{- 2 x - 1}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{3}}\\left(\\frac{25 \\sec{\\left(x \\right)}}{1 - 5 x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 3}\\left(\\frac{2 x^{3}}{2 x - 5}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\pi}\\left(- \\frac{4 \\sec{\\left(x \\right)}}{5 - 4 x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 1}\\left(- \\frac{9 x^{4}}{4 - 3 x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 2}\\left(- \\frac{8}{x^{2} \\left(4 x + 5\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -3}\\left(\\frac{8}{x^{3} \\left(4 x - 3\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -1}\\left(- \\frac{25}{x^{4} \\left(- 4 x - 5\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -1}\\left(- \\frac{15}{x^{2} \\left(5 - 2 x\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -4}\\left(- \\frac{8 x^{3}}{3 - 4 x}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{8 \\cos{\\left(x \\right)}}{4 x + 4}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to \\pi}\\left(- \\frac{6 \\sec{\\left(x \\right)}}{3 x + 2}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -2}\\left(- \\frac{10}{x^{2} \\left(5 x - 2\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 3}\\left(\\frac{9 x^{3}}{x + 2}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 3}\\left(- \\frac{1}{x \\left(x + 2\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{\\sec{\\left(x \\right)}}{x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{2}{x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to -3}\\left(\\frac{4}{x^{3} \\left(4 x + 1\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\pi}\\left(- \\frac{4 \\cot{\\left(x \\right)}}{3 - 2 x}\\right)" ,"options": [ " Continuous " ," Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 1}\\left(\\frac{25 x^{3}}{5 x + 3}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(\\frac{\\cos{\\left(x \\right)}}{- x - 4}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to 1}\\left(\\frac{3}{x^{3} \\left(3 x - 3\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\frac{\\pi}{3}}\\left(\\frac{2 \\sin{\\left(x \\right)}}{x + 4}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to-\\frac{\\pi}{4}}\\left(\\frac{5 \\cos{\\left(x \\right)}}{x - 5}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to -4}\\left(- \\frac{3}{x^{5} \\left(1 - 5 x\\right)}\\right)" ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": "\\lim_{x \\to -3}\\left(\\frac{5}{x^{4} \\left(5 x - 4\\right)}\\right) " ,"options": [ " Continuous " , " Not Continuous "  ], "answer" : "A"},{"question": " \\lim_{x \\to - \\pi}\\left(- \\frac{\\csc{\\left(x \\right)}}{x - 5}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 4}\\left(\\frac{3 x^{4}}{4 - x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\pi}\\left(\\frac{4 \\cot{\\left(x \\right)}}{2 x - 4}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\pi}\\left(\\frac{5 \\cot{\\left(x \\right)}}{- 5 x - 3}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 4}\\left(- \\frac{4}{x^{4} \\left(x - 4\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(- \\frac{16 \\csc{\\left(x \\right)}}{- 4 x - 3}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{9 \\csc{\\left(x \\right)}}{3 x - 1}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(\\frac{6 \\sec{\\left(x \\right)}}{5 - 3 x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(\\frac{5}{x^{3} \\left(5 x - 3\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to -4}\\left(\\frac{16 x}{x + 4}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{8 \\csc{\\left(x \\right)}}{4 x + 5}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{15 \\sec{\\left(x \\right)}}{3 x - 3}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to\\frac{\\pi}{2}}\\left(- \\frac{20 \\tan{\\left(x \\right)}}{- 4 x - 5}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{20 \\tan{\\left(x \\right)}}{5 x - 5}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to -1}\\left(\\frac{9}{x \\left(- 3 x - 3\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(\\frac{9 \\sec{\\left(x \\right)}}{1 - 3 x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{20 \\tan{\\left(x \\right)}}{3 - 5 x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(\\frac{3}{x \\left(- 3 x - 5\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{\\cot{\\left(x \\right)}}{4 - x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 2}\\left(\\frac{4 x^{2}}{2 x - 4}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(\\frac{8}{x \\left(4 x - 1\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(- \\frac{10 \\tan{\\left(x \\right)}}{5 x + 5}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{6}{x^{3} \\left(2 x - 5\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{2\\csc{\\left(x \\right)}}{2 x - 3}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{8 \\cot{\\left(x \\right)}}{4 - 4 x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{3 \\csc{\\left(x\\right)}}{x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 3}\\left(\\frac{x^{3}}{3 - x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ],"answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(\\frac{9 \\csc{\\left(x \\right)}}{3 x - 5}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{4}{x^{3} \\left(- 3 x - 4\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(\\frac{2 \\cot{\\left(x \\right)}}{x - 1}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\pi}\\left(\\frac{10 \\cot{\\left(x \\right)}}{2 x - 2}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\pi}\\left(\\frac{15 \\csc{\\left(x \\right)}}{3 x + 2}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(- \\frac{5 \\cot{\\left(x \\right)}}{- x - 4}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\pi}\\left(- \\frac{10 \\csc{\\left(x \\right)}}{2 x - 4}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\frac{\\pi}{2}}\\left(\\frac{5 \\sec{\\left(x \\right)}}{x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\frac{\\pi}{2}}\\left(- \\frac{10 \\sec{\\left(x \\right)}}{- 2 x - 1}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(\\frac{3}{x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to -2}\\left(\\frac{3 x^{2}}{x + 2}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{20 \\cot{\\left(x \\right)}}{5 x - 1}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to - \\pi}\\left(\\frac{5 \\csc{\\left(x \\right)}}{- x - 5}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(\\frac{25}{x^{5} \\left(- 5 x - 4\\right)}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to \\frac{\\pi}{2}}\\left(- \\frac{3 \\tan{\\left(x \\right)}}{- x - 1}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{5 \\cot{\\left(x \\right)}}{x + 3}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{4 \\cot{\\left(x \\right)}}{- x - 1}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"},{"question": " \\lim_{x \\to 0}\\left(- \\frac{4}{x}\\right)" ,"options": [ " Continuous " , " Not continuous "  ], "answer" : "B"}], "derivative" : [{ "simpleDerivatives" : [{"question": " \\frac{d^{2}}{d x^{2}} 1 " ,"options": [ " 0 " , " 1 " , " 0 " , " 0 " ], "answer": "D" },{"question": " \\frac{d^{2}}{d x^{2}} \\left(4 x^{2} - 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\\frac{5}{x^{3}}\\right) " ,"options": [ " \\frac{15}{x^{4}} " , " \\frac{30}{x^{4}} " , " \\frac{7.5}{x^{4}} " , " \\frac{45}{x^{4}} " ], "answer": "A" },{"question": " \\frac{d^{4}}{d x^{4}} \\left(2 - \\frac{3}{x^{2}}\\right) " ,"options": [ " 1 " , " \\frac{6}{x^{3}} " , " \\frac{3.0}{x^{3}} " , " \\frac{18}{x^{3}} " ], "answer": "B" },{"question": " \\frac{d^{2}}{d x^{2}} \\left(3 x^{2} - 1\\right) " ,"options": [ " 0 " , " 3.0 x " , " 6 x " , " 1 " ], "answer": "C" },{"question": " \\frac{d}{d x} \\left(4 - 5 x^{4}\\right) " ,"options": [ " - 40 x^{3} " , " - 10.0 x^{3} " , " - 20 x^{3} " , " 0 " ], "answer": "C" },{"question": " \\frac{d^{3}}{d x^{3}} \\left(3 x^{3} - 3\\right) " ,"options": [ " 18 x^{2} " , " 4.5 x^{2} " , " 9 x^{2} " , " 0 " ], "answer": "C" },{"question": " \\frac{d^{4}}{d x^{4}} \\left(x^{4} - 1\\right) " ,"options": [ " 4 x^{3} " , " 12 x^{3} " , " 0 " , " 1 " ], "answer": "A" },{"question": " \\frac{d}{d x} \\left(2 - 4 x^{5}\\right) " ,"options": [ " - 10.0 x^{4} " , " - 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