text stringlengths 9 16.2k |
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(-1, 2, 1) \times (-4, -5, -2) = (1, -6, 13) |
\frac{-2}{33} = \frac{-2}{33} |
(0, 0, 5) \times (1, 1, 4) = (-5, 5, 0) |
-1 - 18 = -19 |
-15 + 2 c + c^2 = 0 \implies c \in \{ -5, 3 \} |
f(b) = 1 + 5 b + b^2, \quad g(u) = 1 + 3 u \implies f(g(u)) = 7 + 21 u + 9 u^2 |
7 + c = 0 \implies c = -7 |
f(a) = 2 + 2 a + a^2, \quad g(w) = 4 + 2 w \implies f(g(w)) = 26 + 20 w + 4 w^2 |
\frac{d}{dc}\left(5\right) = 0 |
(1, -5, 5) \times (5, 5, 1) = (-30, 24, 30) |
\log_{4}\left(7 + 3 u\right) = 1 \implies u = -1 |
\int \left(-6 a - 6 \left(-7 + a\right)\right) da = -6 a \left(-7 + a\right) + C |
\log_{2}\left(6 + x\right) = 1 \implies x = -4 |
\frac{42}{9} = \frac{14}{3} |
f(t) = 1 + 2 t + t^2, \quad g(x) = 2 + x \implies f(g(x)) = 9 + 6 x + x^2 |
7 + u = 0 \implies u = -7 |
\frac{d}{dt}\left(t^2 \sin{\left(t\right)}\right) = 2 t \sin{\left(t\right)} + t^2 \cos{\left(t\right)} |
f(t) = 4 + 2 t + t^2, \quad g(z) = 3 + z \implies f(g(z)) = 19 + 8 z + z^2 |
46 + 3 = 49 |
42 \cdot 50 = 2100 |
f(v) = 2 + 4 v + v^2, \quad g(t) = 3 + 2 t \implies f(g(t)) = 23 + 20 t + 4 t^2 |
2 + x = 0 \implies x = -2 |
-2 \cdot 22 = -44 |
f(c) = 3 + 2 c + c^2, \quad g(z) = 3 + z \implies f(g(z)) = 18 + 8 z + z^2 |
-14 + 5 z + z^2 = 0 \implies z \in \{ -7, 2 \} |
f(w) = 1 + 3 w + w^2, \quad g(u) = 4 + 2 u \implies f(g(u)) = 29 + 22 u + 4 u^2 |
-2 + c = 0 \implies c = 2 |
-21 + 4 b + b^2 = 0 \implies b \in \{ -7, 3 \} |
f(x) = 2 + 4 x + x^2, \quad g(v) = 1 + v \implies f(g(v)) = 7 + 6 v + v^2 |
f(a) = 4 + 5 a + a^2, \quad g(x) = 4 + 2 x \implies f(g(x)) = 40 + 26 x + 4 x^2 |
36 \cdot 39 = 1404 |
8 - 9 x + x^2 = 0 \implies x \in \{ 1, 8 \} |
\lim_{t \to 0} \left(\sin{\left(t\right)}\right) = 0 |
32 + 29 = 61 |
1 + y = 0 \implies y = -1 |
-49 + x^2 = 0 \implies x \in \{ -7, 7 \} |
4 + 13 = 17 |
\cos{\left(c\right)} \left(3 + u\right) = u \cos{\left(c\right)} + 3 \cos{\left(c\right)} |
27 - 28 = -1 |
(-3, 4, -2) \times (2, 4, -4) = (-8, -16, -20) |
f(z) = 4 + 3 z + z^2, \quad g(w) = 1 + 2 w \implies f(g(w)) = 8 + 10 w + 4 w^2 |
\int \left(4 t^3\right) dt = t^4 + C |
\frac{13}{26} = \frac{1}{2} |
-56 - u + u^2 = 0 \implies u \in \{ -7, 8 \} |
(5, 1, -2) \times (3, -4, 0) = (-8, -6, -23) |
2 + y = 0 \implies y = -2 |
\log_{5}\left(5 + 3 b\right) = 2 \implies b = \frac{20}{3} |
-30 - w + w^2 = 0 \implies w \in \{ -5, 6 \} |
\left(-5 + y\right) \left(-2 + y\right) = 10 - 7 y + y^2 |
f(x) = 2 + 3 x + x^2, \quad g(v) = 4 + 2 v \implies f(g(v)) = 30 + 22 v + 4 v^2 |
-7 + t = 0 \implies t = 7 |
-8 \cdot 10 = -80 |
\frac{d}{dc}\left(c^3\right) = 3 c^2 |
\frac{-33}{48} = \frac{-11}{16} |
(-1, -1, -5) \times (1, -3, -4) = (-11, -9, 4) |
\log_{5}\left(8 + 3 u\right) = 2 \implies u = \frac{17}{3} |
-2 \left(-9 + c\right) = 18 - 2 c |
\log_{5}\left(3 + 4 x\right) = 2 \implies x = \frac{11}{2} |
x^2 \left(x - y\right) = -x^2 y + x^3 |
28 z + 11 z^2 + z^3 = 0 \implies z \in \{ -7, -4, 0 \} |
\left(c + v\right) c^2 = c^2 v + c^3 |
-20 + 29 u - 10 u^2 + u^3 = 0 \implies u \in \{ 1, 4, 5 \} |
-1 + 19 = 18 |
\lim_{y \to 2} \left(\cos{\left(y\right)}\right) = \cos{\left(2\right)} |
f(b) = 2 + 4 b + b^2, \quad g(u) = 2 + u \implies f(g(u)) = 14 + 8 u + u^2 |
30 - 11 w + w^2 = 0 \implies w \in \{ 5, 6 \} |
-12 + 4 x + 7 x^2 + x^3 = 0 \implies x \in \{ -6, -2, 1 \} |
4 + v = 0 \implies v = -4 |
(5, 4, 1) \times (-2, -4, 1) = (8, -7, -12) |
(0, 0, -5) \times (3, 1, 1) = (5, -15, 0) |
v = 0 \implies v = 0 |
f(w) = 5 + 5 w + w^2, \quad g(c) = 3 + 2 c \implies f(g(c)) = 29 + 22 c + 4 c^2 |
\lim_{t \to -4} \left(-4 t\right) = 16 |
\frac{d}{du}\left(0\right) = 0 |
\int \left(2 x\right) dx = x^2 + C |
\log_{5}\left(5 + t\right) = 2 \implies t = 20 |
\frac{d}{dx}\left(x^2\right) = 2 x |
\log_{4}\left(6 + 4 v\right) = 2 \implies v = \frac{5}{2} |
\log_{4}\left(8 + 4 z\right) = 2 \implies z = 2 |
f(u) = 2 + 5 u + u^2, \quad g(t) = 3 + 2 t \implies f(g(t)) = 26 + 22 t + 4 t^2 |
\log_{5}\left(6 + 4 y\right) = 2 \implies y = \frac{19}{4} |
f(v) = 3 + 4 v + v^2, \quad g(a) = 1 + 3 a \implies f(g(a)) = 8 + 18 a + 9 a^2 |
f(t) = 3 + 4 t + t^2, \quad g(u) = 4 + 3 u \implies f(g(u)) = 35 + 36 u + 9 u^2 |
-39 \cdot 44 = -1716 |
\lim_{b \to -1} \left(0\right) = 0 |
\log_{4}\left(1 + 3 z\right) = 3 \implies z = 21 |
-19 \cdot 43 = -817 |
f(b) = 2 + 3 b + b^2, \quad g(x) = 3 + 3 x \implies f(g(x)) = 20 + 27 x + 9 x^2 |
\log_{3}\left(1 + 3 z\right) = 2 \implies z = \frac{8}{3} |
\int \left(1 - \cos{\left(c\right)}\right) dc = c - \sin{\left(c\right)} + C |
f(v) = 3 + 3 v + v^2, \quad g(t) = 3 + t \implies f(g(t)) = 21 + 9 t + t^2 |
\log_{4}\left(3 + 3 y\right) = 2 \implies y = \frac{13}{3} |
f(w) = 4 + 4 w + w^2, \quad g(v) = 3 + 2 v \implies f(g(v)) = 25 + 20 v + 4 v^2 |
8 \cdot 12 = 96 |
49 + 36 = 85 |
f(v) = 1 + 3 v + v^2, \quad g(x) = 3 + x \implies f(g(x)) = 19 + 9 x + x^2 |
\frac{d}{du}\left(0\right) = 0 |
-6 + b = 0 \implies b = 6 |
f(y) = 2 + 3 y + y^2, \quad g(x) = 1 + 2 x \implies f(g(x)) = 6 + 10 x + 4 x^2 |
-3 + z = 0 \implies z = 3 |
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