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5 + 6 a + a^2 = 0 \implies a \in \{ -5, -1 \} |
4 - 36 = -32 |
\log_{3}\left(5 + 3 c\right) = 1 \implies c = \frac{-2}{3} |
-46 \cdot 37 = -1702 |
\lim_{x \to -3} \left(-6 - x\right) = -3 |
\log_{4}\left(8 + x\right) = 3 \implies x = 56 |
56 + 41 w - 14 w^2 + w^3 = 0 \implies w \in \{ -1, 7, 8 \} |
2 a + a^2 = 0 \implies a \in \{ -2, 0 \} |
\int \left(4 v^3\right) dv = v^4 + C |
\lim_{t \to 3} \left(-8 - t\right) = -11 |
\lim_{x \to 0} \left(10\right) = 10 |
\frac{-23}{12} = \frac{-23}{12} |
43 \cdot 19 = 817 |
-50 + 24 = -26 |
(5, -1, -3) \times (-5, 1, -3) = (6, 30, 0) |
-23 - 44 = -67 |
(2, 2, -2) \times (-4, 5, -5) = (0, 18, 18) |
\frac{d}{du}\left(\cos{\left(u\right)}\right) = -\sin{\left(u\right)} |
f(v) = 5 + 4 v + v^2, \quad g(c) = 3 + 2 c \implies f(g(c)) = 26 + 20 c + 4 c^2 |
\int \left(2 x \sin{\left(x\right)} + x^2 \cos{\left(x\right)}\right) dx = x^2 \sin{\left(x\right)} + C |
(4, 3, 5) \times (0, -2, 0) = (10, 0, -8) |
f(v) = 1 + 4 v + v^2, \quad g(x) = 4 + x \implies f(g(x)) = 33 + 12 x + x^2 |
-6 - 35 = -41 |
-4 v + v^2 = 0 \implies v \in \{ 0, 4 \} |
f(z) = 1 + 2 z + z^2, \quad g(w) = 2 + 3 w \implies f(g(w)) = 9 + 18 w + 9 w^2 |
\int \left(-1\right) db = 9 - \left(9 + b\right) + C |
\lim_{z \to 2} \left(z\right) = 2 |
-14 \cdot 5 = -70 |
280 + 131 b + 20 b^2 + b^3 = 0 \implies b \in \{ -8, -7, -5 \} |
\cos{\left(b\right)} \left(-1 + b\right) = b \cos{\left(b\right)} - \cos{\left(b\right)} |
\frac{d}{dw}\left(w\right) = 1 |
\frac{-8}{14} = \frac{-4}{7} |
-48 - 16 w + 3 w^2 + w^3 = 0 \implies w \in \{ -4, -3, 4 \} |
\log_{3}\left(4 + 2 w\right) = 1 \implies w = \frac{-1}{2} |
-27 - 31 = -58 |
f(z) = 3 + 4 z + z^2, \quad g(c) = 1 + c \implies f(g(c)) = 8 + 6 c + c^2 |
f(z) = 5 + 3 z + z^2, \quad g(v) = 4 + v \implies f(g(v)) = 33 + 11 v + v^2 |
\frac{d}{dv}\left(v\right) = 1 |
3 + 50 = 53 |
40 - 18 u - 3 u^2 + u^3 = 0 \implies u \in \{ -4, 2, 5 \} |
x^2 \left(-8 - x\right) = -8 x^2 - x^3 |
-5 + w = 0 \implies w = 5 |
\frac{43}{31} = \frac{43}{31} |
\log_{5}\left(6 + 4 b\right) = 3 \implies b = \frac{119}{4} |
\frac{d}{db}\left(b^3\right) = 3 b^2 |
f(b) = 5 + 2 b + b^2, \quad g(a) = 1 + 3 a \implies f(g(a)) = 8 + 12 a + 9 a^2 |
\log_{3}\left(5 + 3 a\right) = 1 \implies a = \frac{-2}{3} |
-6 - 32 = -38 |
\sin{\left(u\right)} \left(-10 + u\right) = u \sin{\left(u\right)} - 10 \sin{\left(u\right)} |
\frac{d}{dw}\left(2 w^2\right) = 4 w |
\log_{5}\left(6 + 3 w\right) = 2 \implies w = \frac{19}{3} |
-32 - 4 u + u^2 = 0 \implies u \in \{ -4, 8 \} |
37 - 17 = 20 |
\int \left(2\right) dw = 2 w + C |
-8 + 2 x + x^2 = 0 \implies x \in \{ -4, 2 \} |
\int \left(\sin{\left(x\right)}\right) dx = 1 - \cos{\left(x\right)} + C |
\frac{d}{dw}\left(w\right) = 1 |
\lim_{b \to 0} \left(-5 + b\right) = -5 |
49 - 49 x - x^2 + x^3 = 0 \implies x \in \{ -7, 1, 7 \} |
-32 - 28 t + 5 t^2 + t^3 = 0 \implies t \in \{ -8, -1, 4 \} |
f(y) = 3 + 4 y + y^2, \quad g(c) = 2 + 3 c \implies f(g(c)) = 15 + 24 c + 9 c^2 |
f(b) = 2 + 4 b + b^2, \quad g(y) = 3 + 2 y \implies f(g(y)) = 23 + 20 y + 4 y^2 |
\frac{d}{dt}\left(\cos{\left(t\right)}\right) = -\sin{\left(t\right)} |
\lim_{w \to -3} \left(-5 + w\right) = -8 |
\log_{4}\left(8 + 3 w\right) = 3 \implies w = \frac{56}{3} |
(3, 3, 1) \times (1, 0, 2) = (6, -5, -3) |
f(y) = 4 + 3 y + y^2, \quad g(c) = 4 + 2 c \implies f(g(c)) = 32 + 22 c + 4 c^2 |
f(x) = 1 + 4 x + x^2, \quad g(a) = 2 + 3 a \implies f(g(a)) = 13 + 24 a + 9 a^2 |
\frac{17}{46} = \frac{17}{46} |
\frac{d}{dv}\left(6 - v + v^3\right) = -1 + 3 v^2 |
\frac{24}{49} = \frac{24}{49} |
(3, 3, 2) \times (5, -3, 3) = (15, 1, -24) |
\left(a - t\right) \left(-5 - a\right) = -5 a + 5 t + a t - a^2 |
\frac{d}{dw}\left(w - \sin{\left(w\right)}\right) = 1 - \cos{\left(w\right)} |
\int \left(1\right) dz = z + C |
2 + z = 0 \implies z = -2 |
f(a) = 5 + 2 a + a^2, \quad g(x) = 2 + 3 x \implies f(g(x)) = 13 + 18 x + 9 x^2 |
\log_{4}\left(7 + c\right) = 1 \implies c = -3 |
\int \left(-14 u\right) du = -7 u^2 + C |
\frac{d}{dy}\left(y\right) = 1 |
f(t) = 1 + 2 t + t^2, \quad g(y) = 1 + y \implies f(g(y)) = 4 + 4 y + y^2 |
(4, 1, -1) \times (0, 0, 2) = (2, -8, 0) |
f(z) = 2 + z + z^2, \quad g(a) = 3 + 3 a \implies f(g(a)) = 14 + 21 a + 9 a^2 |
2 - 3 v + v^2 = 0 \implies v \in \{ 1, 2 \} |
-1 + a = 0 \implies a = 1 |
4 + c = 0 \implies c = -4 |
\log_{5}\left(1 + 3 u\right) = 2 \implies u = 8 |
120 - 31 t - 6 t^2 + t^3 = 0 \implies t \in \{ -5, 3, 8 \} |
\frac{d}{db}\left(b^2\right) = 2 b |
\frac{14}{48} = \frac{7}{24} |
\log_{5}\left(6 + 2 x\right) = 3 \implies x = \frac{119}{2} |
\lim_{w \to -2} \left(0\right) = 0 |
(3, -2, 2) \times (5, 5, -2) = (-6, 16, 25) |
-4 + c = 0 \implies c = 4 |
24 + 26 b + 9 b^2 + b^3 = 0 \implies b \in \{ -4, -3, -2 \} |
f(w) = 4 + w + w^2, \quad g(a) = 3 + a \implies f(g(a)) = 16 + 7 a + a^2 |
-6 + v = 0 \implies v = 6 |
\frac{d}{dz}\left(-2 z + z^3\right) = -2 + 3 z^2 |
-1 + c = 0 \implies c = 1 |
8 - 35 = -27 |
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