3 lines
1.6 KiB
JSON
3 lines
1.6 KiB
JSON
{"problem": "$ E = \\left[\\begin{array}{rr}5 & 1 \\\\ 2 & 3\\end{array}\\right]$ What is the determinant of $ E$ ?", "hints": ["The determinant of a 2x2 matrix can be computed the following way:", "$ = $", "In this specific case,", "$ = $", "$ = 13 $"]}
|
|
{"problem": "If $a + b + c = 9$, what is $7c + 7a + 7b$ ?", "hints": ["$= 7a + 7b + 7c$", "$= (7) \\cdot (a + b + c) $", "$= (7) \\cdot (9) $", "$= 63$"]}
|
|
{"problem": "Find $\\lim_{x\\to\\infty}\\dfrac{x^2-4}{\\cos(x)}$. Choose 1 answer: Choose 1 answer: (Choice A) A $4$ (Choice B) B $-2$ (Choice C) C $0$ (Choice D) D The limit doesn't exist", "hints": ["When dealing with limits that include $\\cos(x)$, it's important to remember that $\\lim_{x\\to\\infty}\\cos(x)$ doesn't exist, as $\\cos(x)$ keeps oscillating between $-1$ and $1$ forever. ${2}$ ${4}$ ${6}$ ${8}$ ${\\llap{-}4}$ ${\\llap{-}6}$ ${\\llap{-}8}$ ${2}$ $y$ $x$ $y=\\cos(x)$ This doesn't necessarily mean that our limit doesn't exist. Think what happens to $\\dfrac{x^2-4}{\\cos(x)}$ as $x$ increases towards positive infinity.", "While $x^2-4$ keeps growing boundlessly, $\\cos(x)$ oscillates from $-1$, to $0$, to $1$, to $0$, to $-1$ again. The result is a graph that goes up and down forever, with vertical asymptotes every now and then. ${5}$ ${10}$ ${15}$ ${\\llap{-}5}$ ${\\llap{-}10}$ ${\\llap{-}15}$ ${50}$ ${100}$ ${150}$ ${\\llap{-}50}$ ${\\llap{-}100}$ ${\\llap{-}150}$ $y$ $x$ $y=\\dfrac{x^2-4}{\\cos(x)}$ This limit doesn't approach any specific value as $x$ increases towards infinity.", "In conclusion, $\\lim_{x\\to\\infty}\\dfrac{x^2-4}{\\cos(x)}$ doesn't exist."]} |