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32 + 12 x + x^2 = 0 \implies x \in \{ -8, -4 \} |
\frac{d}{dz}\left(z^4 + \sin{\left(z\right)}\right) = 4 z^3 + \cos{\left(z\right)} |
f(w) = 2 + 2 w + w^2, \quad g(v) = 2 + 3 v \implies f(g(v)) = 10 + 18 v + 9 v^2 |
10 + 7 b + b^2 = 0 \implies b \in \{ -5, -2 \} |
40 w + 13 w^2 + w^3 = 0 \implies w \in \{ -8, -5, 0 \} |
80 + 14 c - 11 c^2 + c^3 = 0 \implies c \in \{ -2, 5, 8 \} |
f(a) = 5 + a + a^2, \quad g(u) = 1 + u \implies f(g(u)) = 7 + 3 u + u^2 |
\lim_{c \to 1} \left(4\right) = 4 |
48 + 44 v + 12 v^2 + v^3 = 0 \implies v \in \{ -6, -4, -2 \} |
-16 - 6 t + t^2 = 0 \implies t \in \{ -2, 8 \} |
-21 - 4 b + b^2 = 0 \implies b \in \{ -3, 7 \} |
\int \left(-4\right) dy = -4 y + C |
-42 - x + x^2 = 0 \implies x \in \{ -6, 7 \} |
150 - 25 w - 6 w^2 + w^3 = 0 \implies w \in \{ -5, 5, 6 \} |
12 a - 7 a^2 + a^3 = 0 \implies a \in \{ 0, 3, 4 \} |
f(b) = 4 + 2 b + b^2, \quad g(x) = 1 + 2 x \implies f(g(x)) = 7 + 8 x + 4 x^2 |
\frac{d}{dz}\left(\sin{\left(z\right)}\right) = \cos{\left(z\right)} |
\frac{-49}{10} = \frac{-49}{10} |
-28 + 30 = 2 |
\frac{18}{41} = \frac{18}{41} |
6 + t = 0 \implies t = -6 |
-3 + x = 0 \implies x = 3 |
31 - 40 = -9 |
\log_{4}\left(8 + 2 w\right) = 3 \implies w = 28 |
43 + 12 = 55 |
-4 a + 3 a^2 + a^3 = 0 \implies a \in \{ -4, 0, 1 \} |
\lim_{t \to 4} \left(t^2\right) = 16 |
f(u) = 1 + u + u^2, \quad g(x) = 3 + x \implies f(g(x)) = 13 + 7 x + x^2 |
-5 + y = 0 \implies y = 5 |
84 + 16 c - 11 c^2 + c^3 = 0 \implies c \in \{ -2, 6, 7 \} |
-39 \cdot 31 = -1209 |
30 - 31 c + c^3 = 0 \implies c \in \{ -6, 1, 5 \} |
-12 + 4 z + 7 z^2 + z^3 = 0 \implies z \in \{ -6, -2, 1 \} |
f(w) = 4 + w + w^2, \quad g(b) = 2 + b \implies f(g(b)) = 10 + 5 b + b^2 |
f(a) = 1 + 2 a + a^2, \quad g(t) = 1 + t \implies f(g(t)) = 4 + 4 t + t^2 |
(-5, 0, 3) \times (3, -1, 5) = (3, 34, 5) |
\log_{5}\left(8 + 4 w\right) = 3 \implies w = \frac{117}{4} |
(-1, 4, -5) \times (0, 3, -1) = (11, -1, -3) |
46 - 46 = 0 |
-3 \cdot 28 = -84 |
\log_{2}\left(3 + 2 y\right) = 1 \implies y = \frac{-1}{2} |
\lim_{u \to -2} \left(u^3\right) = -8 |
f(a) = 2 + 3 a + a^2, \quad g(c) = 2 + c \implies f(g(c)) = 12 + 7 c + c^2 |
-6 + t + t^2 = 0 \implies t \in \{ -3, 2 \} |
(-1, -5, 1) \times (0, -5, -4) = (25, -4, 5) |
56 - 15 y + y^2 = 0 \implies y \in \{ 7, 8 \} |
\frac{d}{dx}\left(-\left(7 + x\right) + \cos{\left(x\right)}\right) = -1 - \sin{\left(x\right)} |
-56 + t + t^2 = 0 \implies t \in \{ -8, 7 \} |
96 - 44 a - 4 a^2 + a^3 = 0 \implies a \in \{ -6, 2, 8 \} |
\log_{5}\left(6 + 2 u\right) = 3 \implies u = \frac{119}{2} |
\lim_{b \to -2} \left(b^2\right) = 4 |
-1 + y = 0 \implies y = 1 |
-24 - 19 z + 6 z^2 + z^3 = 0 \implies z \in \{ -8, -1, 3 \} |
f(u) = 3 + 3 u + u^2, \quad g(x) = 1 + x \implies f(g(x)) = 7 + 5 x + x^2 |
2 v \left(v - z\right) = -2 v z + 2 v^2 |
\log_{5}\left(8 + a\right) = 1 \implies a = -3 |
-6 + t + 4 t^2 + t^3 = 0 \implies t \in \{ -3, -2, 1 \} |
\lim_{v \to 0} \left(v\right) = 0 |
\frac{15}{13} = \frac{15}{13} |
\lim_{u \to 3} \left(\sin{\left(u\right)}\right) = \sin{\left(3\right)} |
f(y) = 1 + 3 y + y^2, \quad g(v) = 1 + 3 v \implies f(g(v)) = 5 + 15 v + 9 v^2 |
24 - 11 c + c^2 = 0 \implies c \in \{ 3, 8 \} |
\lim_{b \to 5} \left(2 b\right) = 10 |
\lim_{b \to 1} \left(-7 + b\right) = -6 |
f(b) = 3 + 5 b + b^2, \quad g(c) = 4 + 2 c \implies f(g(c)) = 39 + 26 c + 4 c^2 |
4 + v = 0 \implies v = -4 |
-1 + a = 0 \implies a = 1 |
\lim_{v \to 0} \left(2 v\right) = 0 |
-18 \cdot 7 = -126 |
(5, -5, -3) \times (2, 5, -5) = (40, 19, 35) |
-6 + c = 0 \implies c = 6 |
f(b) = 2 + 3 b + b^2, \quad g(v) = 1 + 2 v \implies f(g(v)) = 6 + 10 v + 4 v^2 |
-24 v - 2 v^2 + v^3 = 0 \implies v \in \{ -4, 0, 6 \} |
f(w) = 1 + 5 w + w^2, \quad g(c) = 2 + 3 c \implies f(g(c)) = 15 + 27 c + 9 c^2 |
14 + 9 v + v^2 = 0 \implies v \in \{ -7, -2 \} |
29 + 1 = 30 |
f(v) = 5 + 2 v + v^2, \quad g(t) = 4 + t \implies f(g(t)) = 29 + 10 t + t^2 |
(-2, -1, 0) \times (0, -2, 2) = (-2, 4, 4) |
\int \left(1\right) dw = w + C |
(-3, 0, -2) \times (-1, 2, -3) = (4, -7, -6) |
-40 - 3 y + y^2 = 0 \implies y \in \{ -5, 8 \} |
-48 - 14 b + 7 b^2 + b^3 = 0 \implies b \in \{ -8, -2, 3 \} |
f(z) = 4 + z + z^2, \quad g(a) = 1 + a \implies f(g(a)) = 6 + 3 a + a^2 |
\log_{2}\left(1 + 3 v\right) = 1 \implies v = \frac{1}{3} |
\lim_{b \to -5} \left(2 b\right) = -10 |
33 - 2 = 31 |
\frac{d}{dx}\left(-16 x^2\right) = -32 x |
-48 - 2 t + t^2 = 0 \implies t \in \{ -6, 8 \} |
\log_{2}\left(4 + 4 z\right) = 2 \implies z = 0 |
-120 + 74 x - 15 x^2 + x^3 = 0 \implies x \in \{ 4, 5, 6 \} |
\int \left(1\right) du = u + C |
\frac{d}{dt}\left(t^4\right) = 4 t^3 |
3 + z = 0 \implies z = -3 |
\int \left(1 + 4 a^3\right) da = a + a^4 + C |
-144 - 42 a + 5 a^2 + a^3 = 0 \implies a \in \{ -8, -3, 6 \} |
\log_{4}\left(8 + 4 t\right) = 1 \implies t = -1 |
f(t) = 2 + 5 t + t^2, \quad g(u) = 2 + 2 u \implies f(g(u)) = 16 + 18 u + 4 u^2 |
\lim_{c \to -3} \left(7\right) = 7 |
(0, -3, 1) \times (1, -4, 4) = (-8, 1, 3) |
f(t) = 4 + 5 t + t^2, \quad g(z) = 3 + 3 z \implies f(g(z)) = 28 + 33 z + 9 z^2 |
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