text stringlengths 9 16.2k |
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(4, 3, 1) \times (-1, 4, -5) = (-19, 19, 19) |
(-2, -3, 1) \times (0, 0, -5) = (15, -10, 0) |
-2 z + z^2 = 0 \implies z \in \{ 0, 2 \} |
3 + u = 0 \implies u = -3 |
f(u) = 2 + 3 u + u^2, \quad g(y) = 4 + 2 y \implies f(g(y)) = 30 + 22 y + 4 y^2 |
f(c) = 1 + c + c^2, \quad g(v) = 2 + 3 v \implies f(g(v)) = 7 + 15 v + 9 v^2 |
\log_{4}\left(5 + 3 c\right) = 2 \implies c = \frac{11}{3} |
-64 + u^2 = 0 \implies u \in \{ -8, 8 \} |
\frac{1}{6} = \frac{1}{6} |
f(y) = 2 + 4 y + y^2, \quad g(u) = 3 + 3 u \implies f(g(u)) = 23 + 30 u + 9 u^2 |
-7 + y = 0 \implies y = 7 |
\log_{3}\left(3 + 2 w\right) = 2 \implies w = 3 |
\int \left(1\right) dy = y + C |
f(y) = 3 + y + y^2, \quad g(b) = 1 + 3 b \implies f(g(b)) = 5 + 9 b + 9 b^2 |
\lim_{y \to 5} \left(y^2\right) = 25 |
-45 + 40 = -5 |
\int \left(1\right) dy = y + C |
6 - 5 y + y^2 = 0 \implies y \in \{ 2, 3 \} |
f(x) = 3 + 3 x + x^2, \quad g(w) = 4 + w \implies f(g(w)) = 31 + 11 w + w^2 |
f(t) = 2 + 4 t + t^2, \quad g(v) = 3 + 2 v \implies f(g(v)) = 23 + 20 v + 4 v^2 |
\log_{5}\left(6 + c\right) = 3 \implies c = 119 |
\log_{5}\left(5 + 4 a\right) = 2 \implies a = 5 |
8 \cdot 48 = 384 |
30 + 40 = 70 |
24 + 10 w + w^2 = 0 \implies w \in \{ -6, -4 \} |
f(u) = 1 + 3 u + u^2, \quad g(a) = 4 + 3 a \implies f(g(a)) = 29 + 33 a + 9 a^2 |
\int \left(1\right) dv = -10 - \left(-10 - v\right) + C |
(-3, -4, 3) \times (-3, 3, -5) = (11, -24, -21) |
-8 + b = 0 \implies b = 8 |
\frac{d}{db}\left(b^2 - b^3\right) = 2 b - 3 b^2 |
24 - 3 = 21 |
2 + a = 0 \implies a = -2 |
\int \left(2 v\right) dv = v^2 + C |
\log_{4}\left(4 + t\right) = 3 \implies t = 60 |
\lim_{a \to -4} \left(a\right) = -4 |
\log_{2}\left(1 + 4 z\right) = 3 \implies z = \frac{7}{4} |
8 - 45 = -37 |
f(a) = 3 + 4 a + a^2, \quad g(v) = 2 + v \implies f(g(v)) = 15 + 8 v + v^2 |
y^2 \left(7 + b\right) = b y^2 + 7 y^2 |
f(x) = 5 + 2 x + x^2, \quad g(z) = 1 + 2 z \implies f(g(z)) = 8 + 8 z + 4 z^2 |
\frac{d}{dx}\left(x\right) = 1 |
(-1, -2, 4) \times (-4, 3, -4) = (-4, -20, -11) |
\frac{d}{dc}\left(\cos{\left(c\right)}\right) = -\sin{\left(c\right)} |
\lim_{b \to 0} \left(\sin{\left(b\right)}\right) = 0 |
f(u) = 4 + 2 u + u^2, \quad g(b) = 3 + 2 b \implies f(g(b)) = 19 + 16 b + 4 b^2 |
\int \left(1\right) dz = z + C |
-10 - 13 u - 2 u^2 + u^3 = 0 \implies u \in \{ -2, -1, 5 \} |
2 \left(a + v\right) v = 2 a v + 2 v^2 |
\frac{d}{da}\left(\sin{\left(a\right)}\right) = \cos{\left(a\right)} |
w^4 \left(w + y\right) = w^4 y + w^5 |
\log_{4}\left(3 + 4 c\right) = 2 \implies c = \frac{13}{4} |
-11 - 37 = -48 |
\frac{d}{dx}\left(-2\right) = 0 |
\lim_{a \to -3} \left(-5\right) = -5 |
f(c) = 5 + 3 c + c^2, \quad g(w) = 2 + 3 w \implies f(g(w)) = 15 + 21 w + 9 w^2 |
\int \left(-1\right) du = -u + C |
-4 - 3 v + v^2 = 0 \implies v \in \{ -1, 4 \} |
\lim_{v \to 5} \left(2 v\right) = 10 |
-4 + v^2 = 0 \implies v \in \{ -2, 2 \} |
\log_{2}\left(4 + 3 v\right) = 1 \implies v = \frac{-2}{3} |
\log_{5}\left(8 + u\right) = 2 \implies u = 17 |
-48 \cdot 12 = -576 |
\frac{4}{28} = \frac{1}{7} |
\log_{5}\left(8 + t\right) = 1 \implies t = -3 |
\log_{3}\left(5 + w\right) = 1 \implies w = -2 |
\frac{d}{dz}\left(z\right) = 1 |
\lim_{y \to -5} \left(y^2\right) = 25 |
\frac{1}{9} = \frac{1}{9} |
\lim_{w \to 4} \left(w^4\right) = 256 |
\frac{d}{dx}\left(x^3\right) = 3 x^2 |
\frac{d}{dt}\left(t^2 \left(3 + t\right)\right) = 2 t \left(3 + t\right) + t^2 |
\lim_{b \to -4} \left(0\right) = 0 |
(-1, 0, 3) \times (-5, 1, 1) = (-3, -14, -1) |
2 \cdot 40 = 80 |
-39 \cdot 16 = -624 |
\int \left(-\sin{\left(y\right)}\right) dy = -1 + \cos{\left(y\right)} + C |
-28 - 31 t - 2 t^2 + t^3 = 0 \implies t \in \{ -4, -1, 7 \} |
\frac{d}{dt}\left(0\right) = 0 |
-16 + 26 x - 11 x^2 + x^3 = 0 \implies x \in \{ 1, 2, 8 \} |
280 - 51 u - 6 u^2 + u^3 = 0 \implies u \in \{ -7, 5, 8 \} |
\int \left(3 v^2 \cos{\left(v\right)} - v^3 \sin{\left(v\right)}\right) dv = v^3 \cos{\left(v\right)} + C |
\frac{40}{48} = \frac{5}{6} |
f(x) = 1 + 3 x + x^2, \quad g(b) = 1 + 3 b \implies f(g(b)) = 5 + 15 b + 9 b^2 |
-80 + 66 a - 15 a^2 + a^3 = 0 \implies a \in \{ 2, 5, 8 \} |
\int \left(1 + \sin{\left(y\right)}\right) dy = 1 + y - \cos{\left(y\right)} + C |
-20 + y + y^2 = 0 \implies y \in \{ -5, 4 \} |
f(a) = 5 + a + a^2, \quad g(u) = 2 + u \implies f(g(u)) = 11 + 5 u + u^2 |
-2 - a + 2 a^2 + a^3 = 0 \implies a \in \{ -2, -1, 1 \} |
(-4, 0, -4) \times (-3, -2, -3) = (-8, 0, 8) |
\log_{3}\left(5 + 3 t\right) = 2 \implies t = \frac{4}{3} |
\lim_{b \to 5} \left(7\right) = 7 |
\frac{d}{du}\left(-\left(8 + u\right) + u^3\right) = -1 + 3 u^2 |
5 + z = 0 \implies z = -5 |
-2 + w + w^2 = 0 \implies w \in \{ -2, 1 \} |
\lim_{z \to -2} \left(z^3\right) = -8 |
16 \cdot 26 = 416 |
3 + w = 0 \implies w = -3 |
\int \left(-\sin{\left(t\right)}\right) dt = -1 + \cos{\left(t\right)} + C |
\log_{5}\left(7 + 3 v\right) = 1 \implies v = \frac{-2}{3} |
\int \left(2 \cos{\left(z\right)}\right) dz = 2 \sin{\left(z\right)} + C |
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