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f(y) = 4 + y + y^2, \quad g(v) = 2 + 3 v \implies f(g(v)) = 10 + 15 v + 9 v^2 |
\log_{5}\left(5 + 2 y\right) = 1 \implies y = 0 |
\log_{4}\left(5 + 4 y\right) = 3 \implies y = \frac{59}{4} |
f(u) = 1 + 2 u + u^2, \quad g(b) = 2 + 2 b \implies f(g(b)) = 9 + 12 b + 4 b^2 |
\log_{5}\left(5 + 3 b\right) = 2 \implies b = \frac{20}{3} |
\log_{5}\left(2 + 2 b\right) = 1 \implies b = \frac{3}{2} |
-8 + c = 0 \implies c = 8 |
\log_{5}\left(3 + 3 u\right) = 2 \implies u = \frac{22}{3} |
11 + 18 = 29 |
\log_{3}\left(6 + 3 v\right) = 1 \implies v = -1 |
3 + x = 0 \implies x = -3 |
-28 + 19 = -9 |
2 + x = 0 \implies x = -2 |
-34 + 28 = -6 |
-1 + c = 0 \implies c = 1 |
f(c) = 1 + c + c^2, \quad g(w) = 3 + 2 w \implies f(g(w)) = 13 + 14 w + 4 w^2 |
-39 \cdot 18 = -702 |
f(y) = 2 + 2 y + y^2, \quad g(c) = 2 + 3 c \implies f(g(c)) = 10 + 18 c + 9 c^2 |
\lim_{a \to -4} \left(-8\right) = -8 |
(2, -5, -1) \times (0, 0, -4) = (20, 8, 0) |
\frac{d}{dt}\left(t^4\right) = 4 t^3 |
140 + 83 y + 16 y^2 + y^3 = 0 \implies y \in \{ -7, -5, -4 \} |
25 \cdot 19 = 475 |
-3 + z = 0 \implies z = 3 |
\lim_{a \to 5} \left(a^3\right) = 125 |
\log_{4}\left(3 + 2 z\right) = 1 \implies z = \frac{1}{2} |
\log_{5}\left(8 + 4 a\right) = 1 \implies a = \frac{-3}{4} |
\frac{4}{26} = \frac{2}{13} |
\frac{d}{da}\left(a\right) = 1 |
49 + 42 = 91 |
13 - 47 = -34 |
\int \left(1\right) du = u + C |
\int \left(-1\right) dc = -c + C |
-32 + 35 = 3 |
\log_{4}\left(7 + z\right) = 3 \implies z = 57 |
\log_{3}\left(8 + 3 t\right) = 3 \implies t = \frac{19}{3} |
(-2, 5, -4) \times (4, 2, -3) = (-7, -22, -24) |
23 - 40 = -17 |
x \left(2 + x\right) = 2 x + x^2 |
\log_{5}\left(7 + 2 t\right) = 2 \implies t = 9 |
4 + y = 0 \implies y = -4 |
1 \cdot 43 = 43 |
f(a) = 1 + 4 a + a^2, \quad g(c) = 2 + c \implies f(g(c)) = 13 + 8 c + c^2 |
\log_{3}\left(8 + 2 a\right) = 3 \implies a = \frac{19}{2} |
-3 b + b^2 = 0 \implies b \in \{ 0, 3 \} |
\log_{2}\left(7 + 4 w\right) = 1 \implies w = \frac{-5}{4} |
24 + 10 u + u^2 = 0 \implies u \in \{ -6, -4 \} |
-42 - 34 = -76 |
-1 + v = 0 \implies v = 1 |
-48 - 2 z + z^2 = 0 \implies z \in \{ -6, 8 \} |
70 + 59 b + 14 b^2 + b^3 = 0 \implies b \in \{ -7, -5, -2 \} |
\log_{4}\left(5 + 4 v\right) = 2 \implies v = \frac{11}{4} |
f(z) = 5 + 5 z + z^2, \quad g(a) = 3 + 2 a \implies f(g(a)) = 29 + 22 a + 4 a^2 |
\lim_{t \to 3} \left(-3\right) = -3 |
60 + 52 v + 13 v^2 + v^3 = 0 \implies v \in \{ -6, -5, -2 \} |
-14 - 5 w + w^2 = 0 \implies w \in \{ -2, 7 \} |
120 - 14 t - 7 t^2 + t^3 = 0 \implies t \in \{ -4, 5, 6 \} |
\lim_{w \to 4} \left(w^2\right) = 16 |
w^2 \left(-8 + z\right) = w^2 z - 8 w^2 |
-24 - 5 u + u^2 = 0 \implies u \in \{ -3, 8 \} |
(4, -2, -4) \times (-2, 5, -2) = (24, 16, 16) |
-18 - 3 y + y^2 = 0 \implies y \in \{ -3, 6 \} |
f(a) = 3 + 3 a + a^2, \quad g(c) = 4 + c \implies f(g(c)) = 31 + 11 c + c^2 |
\log_{4}\left(7 + 3 v\right) = 3 \implies v = 19 |
\frac{-10}{41} = \frac{-10}{41} |
-24 - 2 y + y^2 = 0 \implies y \in \{ -4, 6 \} |
-19 \cdot 39 = -741 |
f(t) = 2 + t + t^2, \quad g(u) = 3 + u \implies f(g(u)) = 14 + 7 u + u^2 |
-224 - 60 t + 3 t^2 + t^3 = 0 \implies t \in \{ -7, -4, 8 \} |
\frac{31}{47} = \frac{31}{47} |
8 + a = 0 \implies a = -8 |
\int \left(-1 + 3 y^2\right) dy = -y + y^3 + C |
-32 + 13 = -19 |
\int \left(-\sin{\left(t\right)}\right) dt = -1 + \cos{\left(t\right)} + C |
8 + 2 b - 5 b^2 + b^3 = 0 \implies b \in \{ -1, 2, 4 \} |
-2 + t = 0 \implies t = 2 |
\frac{d}{dz}\left(-7\right) = 0 |
-42 - a + a^2 = 0 \implies a \in \{ -6, 7 \} |
\int \left(6 y^5\right) dy = y^6 + C |
6 + 7 t + t^2 = 0 \implies t \in \{ -6, -1 \} |
\lim_{c \to 3} \left(c^4\right) = 81 |
\log_{2}\left(2 + 4 u\right) = 3 \implies u = \frac{3}{2} |
35 \cdot 5 = 175 |
27 - 44 = -17 |
\log_{4}\left(8 + 4 x\right) = 2 \implies x = 2 |
f(w) = 5 + 3 w + w^2, \quad g(t) = 3 + 2 t \implies f(g(t)) = 23 + 18 t + 4 t^2 |
31 - 49 = -18 |
f(z) = 1 + 5 z + z^2, \quad g(u) = 2 + u \implies f(g(u)) = 15 + 9 u + u^2 |
\left(a - y\right) a^2 = -a^2 y + a^3 |
\log_{4}\left(7 + 2 a\right) = 1 \implies a = \frac{-3}{2} |
-17 \cdot 1 = -17 |
\lim_{w \to 0} \left(w\right) = 0 |
44 \cdot 48 = 2112 |
-49 + z^2 = 0 \implies z \in \{ -7, 7 \} |
-10 b + 3 b^2 + b^3 = 0 \implies b \in \{ -5, 0, 2 \} |
\lim_{b \to -5} \left(0\right) = 0 |
f(t) = 4 + 2 t + t^2, \quad g(z) = 2 + 3 z \implies f(g(z)) = 12 + 18 z + 9 z^2 |
\int \left(-3 c^2 - \sin{\left(c\right)}\right) dc = -1 - c^3 + \cos{\left(c\right)} + C |
-40 + 30 = -10 |
\frac{d}{du}\left(u\right) = 1 |
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