text stringlengths 9 16.2k |
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-32 - 4 b + 8 b^2 + b^3 = 0 \implies b \in \{ -8, -2, 2 \} |
\log_{3}\left(6 + 3 a\right) = 2 \implies a = 1 |
-7 + c = 0 \implies c = 7 |
12 + 5 v - 6 v^2 + v^3 = 0 \implies v \in \{ -1, 3, 4 \} |
(1, -2, -1) \times (5, 5, -4) = (13, -1, 15) |
f(z) = 4 + 3 z + z^2, \quad g(t) = 2 + 3 t \implies f(g(t)) = 14 + 21 t + 9 t^2 |
\lim_{c \to -3} \left(\cos{\left(c\right)}\right) = \cos{\left(3\right)} |
-28 - 3 b + b^2 = 0 \implies b \in \{ -4, 7 \} |
\lim_{x \to -1} \left(x\right) = -1 |
f(u) = 3 + 4 u + u^2, \quad g(t) = 3 + 3 t \implies f(g(t)) = 24 + 30 t + 9 t^2 |
-25 + 21 = -4 |
-56 - x + x^2 = 0 \implies x \in \{ -7, 8 \} |
28 + 39 = 67 |
\log_{4}\left(7 + 2 b\right) = 3 \implies b = \frac{57}{2} |
(2, 5, -3) \times (-5, 0, -5) = (-25, 25, 25) |
\lim_{a \to 2} \left(a^2\right) = 4 |
280 - 51 a - 6 a^2 + a^3 = 0 \implies a \in \{ -7, 5, 8 \} |
\lim_{x \to 0} \left(x^2\right) = 0 |
-10 + 45 = 35 |
10 \cdot 15 = 150 |
-29 + 31 = 2 |
\frac{d}{dz}\left(z\right) = 1 |
\int \left(2 z\right) dz = z^2 + C |
\int \left(1\right) dy = y + C |
50 + 14 = 64 |
\log_{5}\left(5 + z\right) = 2 \implies z = 20 |
\lim_{v \to -4} \left(2 v\right) = -8 |
-25 + t^2 = 0 \implies t \in \{ -5, 5 \} |
29 - 22 = 7 |
15 a - 8 a^2 + a^3 = 0 \implies a \in \{ 0, 3, 5 \} |
f(b) = 4 + 2 b + b^2, \quad g(u) = 3 + 3 u \implies f(g(u)) = 19 + 24 u + 9 u^2 |
f(w) = 4 + 3 w + w^2, \quad g(x) = 4 + 2 x \implies f(g(x)) = 32 + 22 x + 4 x^2 |
-1 + x = 0 \implies x = 1 |
\frac{d}{dt}\left(-t^4 + \cos{\left(t\right)}\right) = -4 t^3 - \sin{\left(t\right)} |
-32 \cdot 24 = -768 |
\log_{3}\left(3 + 4 b\right) = 2 \implies b = \frac{3}{2} |
\int \left(4 v^3 \cos{\left(v\right)} - v^4 \sin{\left(v\right)}\right) dv = v^4 \cos{\left(v\right)} + C |
f(t) = 3 + 3 t + t^2, \quad g(z) = 4 + z \implies f(g(z)) = 31 + 11 z + z^2 |
-6 - w + w^2 = 0 \implies w \in \{ -2, 3 \} |
\lim_{t \to -2} \left(t^4\right) = 16 |
f(y) = 1 + 5 y + y^2, \quad g(z) = 3 + 2 z \implies f(g(z)) = 25 + 22 z + 4 z^2 |
\int \left(1\right) dv = v + C |
-1 + w = 0 \implies w = 1 |
-24 + 21 = -3 |
-16 + 6 t + t^2 = 0 \implies t \in \{ -8, 2 \} |
x^4 \left(2 + u\right) = u x^4 + 2 x^4 |
-16 x - 6 x^2 + x^3 = 0 \implies x \in \{ -2, 0, 8 \} |
\lim_{t \to 0} \left(2 + t\right) = 2 |
4 + y = 0 \implies y = -4 |
\log_{4}\left(2 + 3 c\right) = 1 \implies c = \frac{2}{3} |
-1 + v = 0 \implies v = 1 |
\lim_{b \to 5} \left(b\right) = 5 |
\frac{23}{13} = \frac{23}{13} |
\log_{4}\left(6 + v\right) = 1 \implies v = -2 |
-36 \cdot 31 = -1116 |
-6 + 25 = 19 |
f(y) = 2 + y + y^2, \quad g(u) = 2 + 2 u \implies f(g(u)) = 8 + 10 u + 4 u^2 |
\frac{d}{dt}\left(\cos{\left(t\right)}\right) = -\sin{\left(t\right)} |
\log_{2}\left(4 + z\right) = 2 \implies z = 0 |
15 - 8 y + y^2 = 0 \implies y \in \{ 3, 5 \} |
-12 + 4 w + w^2 = 0 \implies w \in \{ -6, 2 \} |
\lim_{b \to 3} \left(b^4\right) = 81 |
\lim_{v \to 1} \left(\sin{\left(v\right)}\right) = \sin{\left(1\right)} |
5 + y = 0 \implies y = -5 |
\frac{-1}{37} = \frac{-1}{37} |
f(a) = 5 + 3 a + a^2, \quad g(z) = 2 + 3 z \implies f(g(z)) = 15 + 21 z + 9 z^2 |
\lim_{z \to -5} \left(z\right) = -5 |
-1 + y = 0 \implies y = 1 |
24 - 40 = -16 |
-40 + 27 v + 12 v^2 + v^3 = 0 \implies v \in \{ -8, -5, 1 \} |
6 - 5 x + x^2 = 0 \implies x \in \{ 2, 3 \} |
\log_{5}\left(4 + t\right) = 1 \implies t = 1 |
-36 - 34 = -70 |
\int \left(1\right) dy = y + C |
\left(-b + u\right) \left(b + u\right) = -b^2 + u^2 |
-14 \cdot 32 = -448 |
c^2 \left(4 + c\right) = 4 c^2 + c^3 |
-24 - 5 c + c^2 = 0 \implies c \in \{ -3, 8 \} |
20 + 11 v - 8 v^2 + v^3 = 0 \implies v \in \{ -1, 4, 5 \} |
\log_{4}\left(2 + 2 v\right) = 3 \implies v = 31 |
(-2, -3, -4) \times (-2, 2, -3) = (17, 2, -10) |
-2 + t = 0 \implies t = 2 |
-32 \cdot 22 = -704 |
\frac{-44}{36} = \frac{-11}{9} |
4 + c = 0 \implies c = -4 |
\lim_{a \to 0} \left(a^2\right) = 0 |
\frac{d}{dv}\left(3 v\right) = 3 |
20 - 16 = 4 |
\lim_{u \to 2} \left(0\right) = 0 |
f(y) = 2 + 2 y + y^2, \quad g(t) = 1 + 3 t \implies f(g(t)) = 5 + 12 t + 9 t^2 |
f(v) = 4 + v + v^2, \quad g(u) = 4 + 2 u \implies f(g(u)) = 24 + 18 u + 4 u^2 |
\frac{d}{dc}\left(9 + \cos{\left(c\right)}\right) = -\sin{\left(c\right)} |
f(w) = 5 + w + w^2, \quad g(a) = 2 + 2 a \implies f(g(a)) = 11 + 10 a + 4 a^2 |
\int \left(-\sin{\left(v\right)}\right) dv = -1 + \cos{\left(v\right)} + C |
\int \left(1\right) db = b + C |
f(c) = 3 + 3 c + c^2, \quad g(z) = 4 + z \implies f(g(z)) = 31 + 11 z + z^2 |
-10 \cdot 11 = -110 |
f(b) = 4 + 2 b + b^2, \quad g(u) = 4 + u \implies f(g(u)) = 28 + 10 u + u^2 |
\int \left(\cos{\left(y\right)}\right) dy = \sin{\left(y\right)} + C |
7 - 8 w + w^2 = 0 \implies w \in \{ 1, 7 \} |
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