text stringlengths 9 16.2k |
|---|
f(y) = 5 + 2 y + y^2, \quad g(u) = 1 + 3 u \implies f(g(u)) = 8 + 12 u + 9 u^2 |
f(w) = 2 + w + w^2, \quad g(b) = 1 + b \implies f(g(b)) = 4 + 3 b + b^2 |
1 + u = 0 \implies u = -1 |
34 + 42 = 76 |
f(x) = 3 + 4 x + x^2, \quad g(w) = 4 + w \implies f(g(w)) = 35 + 12 w + w^2 |
\lim_{u \to 3} \left(-10 u\right) = -30 |
-4 + c = 0 \implies c = 4 |
\log_{2}\left(2 + 2 x\right) = 1 \implies x = 0 |
\lim_{a \to -3} \left(-a\right) = 3 |
\log_{4}\left(8 + 3 x\right) = 2 \implies x = \frac{8}{3} |
\log_{5}\left(8 + 2 v\right) = 1 \implies v = \frac{-3}{2} |
(-1, 2, 5) \times (0, -3, -5) = (5, -5, 3) |
\frac{d}{dt}\left(\cos{\left(t\right)}\right) = -\sin{\left(t\right)} |
\log_{5}\left(7 + 3 u\right) = 1 \implies u = \frac{-2}{3} |
\log_{5}\left(5 + 2 b\right) = 1 \implies b = 0 |
280 + 131 u + 20 u^2 + u^3 = 0 \implies u \in \{ -8, -7, -5 \} |
\int \left(1\right) du = u + C |
\int \left(3 y^2\right) dy = y^3 + C |
3 - 38 = -35 |
\frac{d}{dt}\left(t^3\right) = 3 t^2 |
(-4, -2, 1) \times (-5, -1, 0) = (1, -5, -6) |
f(z) = 2 + 4 z + z^2, \quad g(u) = 3 + u \implies f(g(u)) = 23 + 10 u + u^2 |
-14 + 6 = -8 |
-46 - 38 = -84 |
-6 + w = 0 \implies w = 6 |
-\left(2 + t\right) = -2 - t |
\lim_{z \to 1} \left(4 - z\right) = 3 |
\int \left(5 z^4\right) dz = z^5 + C |
f(t) = 4 + 4 t + t^2, \quad g(a) = 2 + a \implies f(g(a)) = 16 + 8 a + a^2 |
\log_{5}\left(4 + 2 t\right) = 2 \implies t = \frac{21}{2} |
2 a + a^2 = 0 \implies a \in \{ -2, 0 \} |
40 \cdot 46 = 1840 |
-3 + 36 = 33 |
150 - 25 y - 6 y^2 + y^3 = 0 \implies y \in \{ -5, 5, 6 \} |
\left(u + x\right) \left(-1 + x\right) = -u - x + u x + x^2 |
48 - 50 a + a^2 + a^3 = 0 \implies a \in \{ -8, 1, 6 \} |
\int \left(\cos{\left(v\right)}\right) dv = \sin{\left(v\right)} + C |
3 + t = 0 \implies t = -3 |
50 - 49 = 1 |
-4 - 12 = -16 |
\frac{d}{da}\left(\cos{\left(a\right)}\right) = -\sin{\left(a\right)} |
\lim_{x \to 0} \left(-28\right) = -28 |
8 + 14 a + 7 a^2 + a^3 = 0 \implies a \in \{ -4, -2, -1 \} |
98 - 49 v - 2 v^2 + v^3 = 0 \implies v \in \{ -7, 2, 7 \} |
f(u) = 1 + u + u^2, \quad g(z) = 4 + z \implies f(g(z)) = 21 + 9 z + z^2 |
\frac{-24}{26} = \frac{-12}{13} |
\frac{-12}{7} = \frac{-12}{7} |
f(x) = 3 + 5 x + x^2, \quad g(v) = 4 + 3 v \implies f(g(v)) = 39 + 39 v + 9 v^2 |
105 + 71 t + 15 t^2 + t^3 = 0 \implies t \in \{ -7, -5, -3 \} |
-13 \cdot 12 = -156 |
\frac{d}{dz}\left(z^2\right) = 2 z |
43 - 18 = 25 |
f(u) = 4 + u + u^2, \quad g(v) = 2 + 2 v \implies f(g(v)) = 10 + 10 v + 4 v^2 |
-2 + t = 0 \implies t = 2 |
\log_{4}\left(3 + x\right) = 1 \implies x = 1 |
\frac{7}{36} = \frac{7}{36} |
-21 + 4 v + v^2 = 0 \implies v \in \{ -7, 3 \} |
f(z) = 1 + z + z^2, \quad g(v) = 3 + 3 v \implies f(g(v)) = 13 + 21 v + 9 v^2 |
-32 - 4 x + x^2 = 0 \implies x \in \{ -4, 8 \} |
-35 - 2 t + t^2 = 0 \implies t \in \{ -5, 7 \} |
f(a) = 2 + 5 a + a^2, \quad g(t) = 2 + 3 t \implies f(g(t)) = 16 + 27 t + 9 t^2 |
\log_{2}\left(2 + 3 y\right) = 1 \implies y = 0 |
\log_{3}\left(4 + b\right) = 1 \implies b = -1 |
6 - 7 a + a^2 = 0 \implies a \in \{ 1, 6 \} |
\frac{d}{dy}\left(\sin{\left(y\right)}\right) = \cos{\left(y\right)} |
\log_{3}\left(6 + 2 t\right) = 3 \implies t = \frac{21}{2} |
(4, -5, 3) \times (-4, -5, 0) = (15, -12, -40) |
f(a) = 5 + a + a^2, \quad g(y) = 1 + 2 y \implies f(g(y)) = 7 + 6 y + 4 y^2 |
3 - 4 x + x^2 = 0 \implies x \in \{ 1, 3 \} |
f(t) = 4 + 3 t + t^2, \quad g(c) = 4 + c \implies f(g(c)) = 32 + 11 c + c^2 |
-5 \cdot 8 = -40 |
41 + 30 = 71 |
(-4, -1, -4) \times (5, 3, -5) = (17, -40, -7) |
\log_{2}\left(8 + 2 x\right) = 1 \implies x = -3 |
6 + 5 y + y^2 = 0 \implies y \in \{ -3, -2 \} |
\sin{\left(c\right)} \left(6 + c\right) = c \sin{\left(c\right)} + 6 \sin{\left(c\right)} |
f(c) = 2 + 2 c + c^2, \quad g(y) = 3 + 3 y \implies f(g(y)) = 17 + 24 y + 9 y^2 |
f(z) = 3 + 5 z + z^2, \quad g(v) = 3 + 3 v \implies f(g(v)) = 27 + 33 v + 9 v^2 |
18 + 23 = 41 |
-21 \cdot 27 = -567 |
f(t) = 5 + 5 t + t^2, \quad g(u) = 2 + 3 u \implies f(g(u)) = 19 + 27 u + 9 u^2 |
\log_{3}\left(8 + 2 w\right) = 3 \implies w = \frac{19}{2} |
-20 - x + x^2 = 0 \implies x \in \{ -4, 5 \} |
\frac{d}{dz}\left(z^2 + \sin{\left(z\right)}\right) = 2 z + \cos{\left(z\right)} |
-21 + 25 = 4 |
-5 + 41 = 36 |
28 - 11 u + u^2 = 0 \implies u \in \{ 4, 7 \} |
17 + 42 = 59 |
x^2 \left(u - x\right) = u x^2 - x^3 |
15 + 35 = 50 |
-24 \cdot 43 = -1032 |
\frac{d}{du}\left(u^5\right) = 5 u^4 |
-42 + 55 v - 14 v^2 + v^3 = 0 \implies v \in \{ 1, 6, 7 \} |
-14 + 23 v - 10 v^2 + v^3 = 0 \implies v \in \{ 1, 2, 7 \} |
\lim_{x \to 2} \left(x^2\right) = 4 |
10 \cdot 46 = 460 |
\frac{d}{dx}\left(x - x^4\right) = 1 - 4 x^3 |
\frac{d}{dv}\left(2 v - v^4\right) = 2 - 4 v^3 |
14 + 9 u + u^2 = 0 \implies u \in \{ -7, -2 \} |
40 - 47 = -7 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.