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-2 w + w^2 = 0 \implies w \in \{ 0, 2 \} |
\left(u + w\right) \sin{\left(w\right)} = u \sin{\left(w\right)} + w \sin{\left(w\right)} |
\frac{47}{36} = \frac{47}{36} |
y \left(-3 + y\right) = -3 y + y^2 |
-30 - 31 u + u^3 = 0 \implies u \in \{ -5, -1, 6 \} |
\frac{-47}{29} = \frac{-47}{29} |
6 y + y^2 = 0 \implies y \in \{ -6, 0 \} |
-24 \cdot 16 = -384 |
-2 + v = 0 \implies v = 2 |
f(v) = 1 + 4 v + v^2, \quad g(y) = 3 + y \implies f(g(y)) = 22 + 10 y + y^2 |
f(t) = 4 + 3 t + t^2, \quad g(x) = 2 + 3 x \implies f(g(x)) = 14 + 21 x + 9 x^2 |
(2, 5, 0) \times (4, -1, 3) = (15, -6, -22) |
7 + b = 0 \implies b = -7 |
42 + 4 = 46 |
\log_{4}\left(5 + 3 x\right) = 1 \implies x = \frac{-1}{3} |
-21 + 21 = 0 |
f(u) = 3 + 4 u + u^2, \quad g(b) = 2 + 3 b \implies f(g(b)) = 15 + 24 b + 9 b^2 |
-36 + 37 = 1 |
-1 + b = 0 \implies b = 1 |
-7 + 6 t + t^2 = 0 \implies t \in \{ -7, 1 \} |
-21 + 4 y + y^2 = 0 \implies y \in \{ -7, 3 \} |
v \left(1 - u\right) = v - u v |
-42 + 11 = -31 |
-41 - 24 = -65 |
15 + 8 c + c^2 = 0 \implies c \in \{ -5, -3 \} |
(1, -1, -4) \times (5, 2, 2) = (6, -22, 7) |
\lim_{u \to -4} \left(u^2\right) = 16 |
f(v) = 5 + 3 v + v^2, \quad g(u) = 2 + u \implies f(g(u)) = 15 + 7 u + u^2 |
\int \left(2 a - \sin{\left(a\right)}\right) da = -1 + a^2 + \cos{\left(a\right)} + C |
-18 - 3 u + u^2 = 0 \implies u \in \{ -3, 6 \} |
-16 + 6 v + v^2 = 0 \implies v \in \{ -8, 2 \} |
\lim_{t \to 3} \left(t^2\right) = 9 |
\frac{-38}{10} = \frac{-19}{5} |
-14 \cdot 22 = -308 |
\log_{3}\left(6 + 4 w\right) = 2 \implies w = \frac{3}{4} |
\lim_{w \to -5} \left(-w\right) = 5 |
\frac{22}{35} = \frac{22}{35} |
(1, 3, 5) \times (-1, 1, -1) = (-8, -4, 4) |
-42 \cdot 44 = -1848 |
28 + 39 x + 12 x^2 + x^3 = 0 \implies x \in \{ -7, -4, -1 \} |
35 + 12 a + a^2 = 0 \implies a \in \{ -7, -5 \} |
f(t) = 5 + 5 t + t^2, \quad g(u) = 1 + 2 u \implies f(g(u)) = 11 + 14 u + 4 u^2 |
\frac{d}{dc}\left(-9 c + \cos{\left(c\right)}\right) = -9 - \sin{\left(c\right)} |
-1 - 8 = -9 |
f(b) = 2 + 4 b + b^2, \quad g(v) = 1 + v \implies f(g(v)) = 7 + 6 v + v^2 |
3 - 34 = -31 |
\frac{d}{dy}\left(1 + y\right) = 1 |
\int \left(-2 - \sin{\left(w\right)}\right) dw = -1 - 2 w + \cos{\left(w\right)} + C |
-4 + 3 v + v^2 = 0 \implies v \in \{ -4, 1 \} |
-1 + z = 0 \implies z = 1 |
3 b + 4 b^2 + b^3 = 0 \implies b \in \{ -3, -1, 0 \} |
\log_{5}\left(7 + 3 c\right) = 1 \implies c = \frac{-2}{3} |
\log_{4}\left(3 + 4 a\right) = 1 \implies a = \frac{1}{4} |
\frac{-6}{8} = \frac{-3}{4} |
-38 \cdot 5 = -190 |
(4, -3, -5) \times (-4, 0, 3) = (-9, 8, -12) |
f(t) = 1 + 2 t + t^2, \quad g(y) = 4 + y \implies f(g(y)) = 25 + 10 y + y^2 |
-48 + 2 u + u^2 = 0 \implies u \in \{ -8, 6 \} |
\int \left(-1 + 3 x^2\right) dx = 9 - \left(9 + x\right) + x^3 + C |
\frac{d}{da}\left(a^3\right) = 3 a^2 |
(-1, -3, 1) \times (0, 1, 3) = (-10, 3, -1) |
1 + z = 0 \implies z = -1 |
-7 + y = 0 \implies y = 7 |
22 + 19 = 41 |
f(y) = 5 + 2 y + y^2, \quad g(w) = 1 + 2 w \implies f(g(w)) = 8 + 8 w + 4 w^2 |
f(z) = 3 + 3 z + z^2, \quad g(t) = 3 + 2 t \implies f(g(t)) = 21 + 18 t + 4 t^2 |
\frac{d}{db}\left(-1 - 2 b\right) = -2 |
\lim_{y \to 0} \left(2 y\right) = 0 |
f(y) = 5 + 2 y + y^2, \quad g(x) = 2 + x \implies f(g(x)) = 13 + 6 x + x^2 |
\frac{-28}{30} = \frac{-14}{15} |
48 - 46 z - 3 z^2 + z^3 = 0 \implies z \in \{ -6, 1, 8 \} |
\int \left(1\right) dt = t + C |
\int \left(4 v^3 \sin{\left(v\right)} + v^4 \cos{\left(v\right)}\right) dv = v^4 \sin{\left(v\right)} + C |
28 - 11 t + t^2 = 0 \implies t \in \{ 4, 7 \} |
\log_{4}\left(5 + 2 a\right) = 2 \implies a = \frac{11}{2} |
-41 + 33 = -8 |
f(z) = 3 + z + z^2, \quad g(w) = 4 + w \implies f(g(w)) = 23 + 9 w + w^2 |
(2, 0, 0) \times (-4, -2, 2) = (0, -4, -4) |
\sin{\left(b\right)} \left(-3 + b\right) = b \sin{\left(b\right)} - 3 \sin{\left(b\right)} |
\log_{2}\left(5 + 4 c\right) = 1 \implies c = \frac{-3}{4} |
f(t) = 3 + 2 t + t^2, \quad g(u) = 3 + 3 u \implies f(g(u)) = 18 + 24 u + 9 u^2 |
f(b) = 5 + b + b^2, \quad g(x) = 1 + 3 x \implies f(g(x)) = 7 + 9 x + 9 x^2 |
f(a) = 5 + 3 a + a^2, \quad g(x) = 3 + 3 x \implies f(g(x)) = 23 + 27 x + 9 x^2 |
6 + z = 0 \implies z = -6 |
f(v) = 5 + 5 v + v^2, \quad g(c) = 2 + c \implies f(g(c)) = 19 + 9 c + c^2 |
-46 + 22 = -24 |
-6 - u + u^2 = 0 \implies u \in \{ -2, 3 \} |
\lim_{v \to 5} \left(8 - v\right) = 3 |
30 - 11 c + c^2 = 0 \implies c \in \{ 5, 6 \} |
-2 + z = 0 \implies z = 2 |
\frac{d}{db}\left(b\right) = 1 |
1 + b = 0 \implies b = -1 |
\log_{5}\left(4 + 4 a\right) = 2 \implies a = \frac{21}{4} |
f(w) = 1 + 2 w + w^2, \quad g(z) = 2 + 3 z \implies f(g(z)) = 9 + 18 z + 9 z^2 |
\log_{4}\left(3 + 4 a\right) = 2 \implies a = \frac{13}{4} |
(1, 0, 0) \times (-3, 2, 1) = (0, -1, 2) |
-4 + x = 0 \implies x = 4 |
(-3, -3, 5) \times (1, -4, 3) = (11, 14, 15) |
\frac{-27}{46} = \frac{-27}{46} |
31 \cdot 4 = 124 |
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