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\log_{3}\left(8 + 4 c\right) = 3 \implies c = \frac{19}{4} |
1 + a = 0 \implies a = -1 |
-6 + v = 0 \implies v = 6 |
40 - 8 = 32 |
\int \left(4 z^3\right) dz = z^4 + C |
t v \left(-9 - v\right) = -9 t v - t v^2 |
-5 b + b^2 = 0 \implies b \in \{ 0, 5 \} |
\frac{d}{dz}\left(7 - z - \left(9 + z\right)\right) = -2 |
\log_{2}\left(8 + 3 x\right) = 3 \implies x = 0 |
f(w) = 3 + 4 w + w^2, \quad g(c) = 2 + c \implies f(g(c)) = 15 + 8 c + c^2 |
\frac{d}{dv}\left(v^4\right) = 4 v^3 |
\frac{-7}{25} = \frac{-7}{25} |
z \left(3 + z\right) = 3 z + z^2 |
25 + 4 = 29 |
(2, -1, 3) \times (2, -3, -1) = (10, 8, -4) |
\int \left(-\sin{\left(u\right)}\right) du = -1 + \cos{\left(u\right)} + C |
\int \left(2\right) dv = 2 v + C |
33 - 16 = 17 |
7 - 8 v + v^2 = 0 \implies v \in \{ 1, 7 \} |
f(y) = 4 + 4 y + y^2, \quad g(a) = 1 + a \implies f(g(a)) = 9 + 6 a + a^2 |
f(w) = 3 + 2 w + w^2, \quad g(u) = 2 + 3 u \implies f(g(u)) = 11 + 18 u + 9 u^2 |
-47 - 33 = -80 |
\log_{5}\left(8 + y\right) = 1 \implies y = -3 |
f(z) = 1 + 3 z + z^2, \quad g(v) = 1 + v \implies f(g(v)) = 5 + 5 v + v^2 |
-4 - 31 = -35 |
-70 + 11 c + 10 c^2 + c^3 = 0 \implies c \in \{ -7, -5, 2 \} |
\lim_{u \to -5} \left(2 u\right) = -10 |
\int \left(\cos{\left(y\right)}\right) dy = \sin{\left(y\right)} + C |
\frac{32}{47} = \frac{32}{47} |
(-1, 0, 0) \times (-4, -3, 5) = (0, 5, 3) |
8 - 9 w + w^2 = 0 \implies w \in \{ 1, 8 \} |
28 \cdot 39 = 1092 |
\log_{2}\left(1 + 2 y\right) = 3 \implies y = \frac{7}{2} |
\lim_{c \to -1} \left(c\right) = -1 |
-48 - 2 w + w^2 = 0 \implies w \in \{ -6, 8 \} |
35 \cdot 24 = 840 |
\frac{-38}{38} = -1 |
\frac{d}{dx}\left(x^2 - \sin{\left(x\right)}\right) = 2 x - \cos{\left(x\right)} |
\frac{d}{dx}\left(x \sin{\left(x\right)}\right) = x \cos{\left(x\right)} + \sin{\left(x\right)} |
\frac{44}{12} = \frac{11}{3} |
(-4, -5, -5) \times (-1, 2, 0) = (10, 5, -13) |
\log_{3}\left(4 + 2 a\right) = 1 \implies a = \frac{-1}{2} |
84 - 44 z - z^2 + z^3 = 0 \implies z \in \{ -7, 2, 6 \} |
\log_{4}\left(7 + 2 v\right) = 1 \implies v = \frac{-3}{2} |
5 + b = 0 \implies b = -5 |
-20 + y + y^2 = 0 \implies y \in \{ -5, 4 \} |
\lim_{w \to -2} \left(4 + w\right) = 2 |
6 \cdot 1 = 6 |
-40 a - 3 a^2 + a^3 = 0 \implies a \in \{ -5, 0, 8 \} |
u = 0 \implies u = 0 |
\lim_{z \to -3} \left(-2\right) = -2 |
\int \left(-1 + 2 z\right) dz = -z + z^2 + C |
\int \left(1\right) dv = v + C |
8 + t = 0 \implies t = -8 |
f(x) = 1 + 3 x + x^2, \quad g(w) = 2 + w \implies f(g(w)) = 11 + 7 w + w^2 |
\int \left(1\right) dw = w + C |
\frac{d}{dy}\left(-2 y + y^4\right) = -2 + 4 y^3 |
\frac{2}{10} = \frac{1}{5} |
\frac{d}{dw}\left(\cos{\left(w\right)}\right) = -\sin{\left(w\right)} |
-20 - c + c^2 = 0 \implies c \in \{ -4, 5 \} |
\lim_{b \to 3} \left(0\right) = 0 |
\frac{d}{dx}\left(-4 x + x^2\right) = -4 + 2 x |
\log_{2}\left(6 + 4 t\right) = 2 \implies t = \frac{-1}{2} |
\log_{2}\left(7 + 4 c\right) = 2 \implies c = \frac{-3}{4} |
6 z + z^2 = 0 \implies z \in \{ -6, 0 \} |
\log_{3}\left(6 + 4 x\right) = 3 \implies x = \frac{21}{4} |
-1 + w = 0 \implies w = 1 |
\int \left(1 - \sin{\left(b\right)}\right) db = -1 + b + \cos{\left(b\right)} + C |
-41 - 10 = -51 |
\frac{d}{dy}\left(y\right) = 1 |
(-1, 5, 5) \times (4, 4, 3) = (-5, 23, -24) |
f(t) = 3 + 5 t + t^2, \quad g(c) = 4 + 2 c \implies f(g(c)) = 39 + 26 c + 4 c^2 |
3 + z = 0 \implies z = -3 |
\frac{d}{dc}\left(c^3\right) = 3 c^2 |
-64 + u^2 = 0 \implies u \in \{ -8, 8 \} |
5 \left(-2 - w\right) = -10 - 5 w |
-32 - 21 = -53 |
f(c) = 3 + c + c^2, \quad g(z) = 4 + z \implies f(g(z)) = 23 + 9 z + z^2 |
\frac{d}{dw}\left(0\right) = 0 |
\lim_{b \to 3} \left(b^4\right) = 81 |
\lim_{u \to -4} \left(\sin{\left(u\right)}\right) = -\sin{\left(4\right)} |
\int \left(3 w^2\right) dw = w^3 + C |
\frac{43}{43} = 1 |
f(v) = 3 + 3 v + v^2, \quad g(c) = 4 + c \implies f(g(c)) = 31 + 11 c + c^2 |
\lim_{c \to 3} \left(8\right) = 8 |
\frac{d}{da}\left(a\right) = 1 |
(2, -5, -3) \times (-2, -3, -4) = (11, 14, -16) |
f(y) = 4 + 3 y + y^2, \quad g(x) = 4 + x \implies f(g(x)) = 32 + 11 x + x^2 |
-144 + 6 z + 11 z^2 + z^3 = 0 \implies z \in \{ -8, -6, 3 \} |
-42 + t + t^2 = 0 \implies t \in \{ -7, 6 \} |
\log_{3}\left(5 + 2 y\right) = 1 \implies y = -1 |
-16 - 10 w + 7 w^2 + w^3 = 0 \implies w \in \{ -8, -1, 2 \} |
\lim_{u \to 3} \left(\sin{\left(u\right)}\right) = \sin{\left(3\right)} |
\log_{5}\left(1 + 3 u\right) = 2 \implies u = 8 |
\log_{4}\left(6 + 3 a\right) = 3 \implies a = \frac{58}{3} |
\frac{d}{dt}\left(2 t + t^2\right) = 2 + 2 t |
-23 - 19 = -42 |
38 - 31 = 7 |
34 + 13 = 47 |
\lim_{v \to 5} \left(-10 - v\right) = -15 |
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