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f(v) = 3 + v + v^2, \quad g(a) = 2 + a \implies f(g(a)) = 9 + 5 a + a^2 |
\left(a + w\right) a^3 = a^3 w + a^4 |
\frac{d}{dy}\left(-8 y\right) = -8 |
\int \left(1 - \sin{\left(c\right)}\right) dc = -1 + c + \cos{\left(c\right)} + C |
(-5, 1, 3) \times (-4, -2, 3) = (9, 3, 14) |
\log_{4}\left(4 + z\right) = 1 \implies z = 0 |
\log_{3}\left(1 + 2 u\right) = 3 \implies u = 13 |
\lim_{u \to 2} \left(0\right) = 0 |
f(a) = 4 + 4 a + a^2, \quad g(z) = 2 + z \implies f(g(z)) = 16 + 8 z + z^2 |
\frac{d}{dw}\left(w^3\right) = 3 w^2 |
12 + 18 = 30 |
-11 + 48 = 37 |
(3, -5, 1) \times (-5, 3, 1) = (-8, -8, -16) |
33 + 9 = 42 |
f(b) = 1 + 2 b + b^2, \quad g(w) = 3 + 2 w \implies f(g(w)) = 16 + 16 w + 4 w^2 |
4 + b = 0 \implies b = -4 |
\frac{33}{44} = \frac{3}{4} |
f(w) = 4 + w + w^2, \quad g(c) = 4 + 3 c \implies f(g(c)) = 24 + 27 c + 9 c^2 |
-44 + 30 = -14 |
\lim_{c \to -2} \left(c^2\right) = 4 |
\log_{4}\left(6 + 4 x\right) = 1 \implies x = \frac{-1}{2} |
-140 - 13 y + 8 y^2 + y^3 = 0 \implies y \in \{ -7, -5, 4 \} |
\frac{d}{dc}\left(c^3\right) = 3 c^2 |
(-2, -3, 4) \times (1, 5, -4) = (-8, -4, -7) |
\lim_{v \to 4} \left(v^4\right) = 256 |
48 \cdot 22 = 1056 |
\lim_{u \to -4} \left(u^3\right) = -64 |
-96 + 20 v + 12 v^2 + v^3 = 0 \implies v \in \{ -8, -6, 2 \} |
28 + 17 v - 10 v^2 + v^3 = 0 \implies v \in \{ -1, 4, 7 \} |
\int \left(1 - \sin{\left(v\right)}\right) dv = -1 + v + \cos{\left(v\right)} + C |
\log_{4}\left(6 + 4 c\right) = 3 \implies c = \frac{29}{2} |
\int \left(1\right) dv = v + C |
\log_{3}\left(8 + 3 a\right) = 2 \implies a = \frac{1}{3} |
\frac{30}{47} = \frac{30}{47} |
\log_{5}\left(6 + 4 a\right) = 1 \implies a = \frac{-1}{4} |
\log_{2}\left(5 + v\right) = 1 \implies v = -3 |
\log_{5}\left(8 + 3 x\right) = 1 \implies x = -1 |
4 + 14 = 18 |
\log_{5}\left(4 + x\right) = 3 \implies x = 121 |
28 + 1 = 29 |
\left(-v + y\right) \left(-4 + y\right) = 4 v - 4 y - v y + y^2 |
f(x) = 3 + 5 x + x^2, \quad g(w) = 3 + 2 w \implies f(g(w)) = 27 + 22 w + 4 w^2 |
\frac{48}{4} = 12 |
f(a) = 1 + 3 a + a^2, \quad g(w) = 1 + w \implies f(g(w)) = 5 + 5 w + w^2 |
\log_{3}\left(3 + 2 v\right) = 3 \implies v = 12 |
\log_{2}\left(2 + 4 z\right) = 1 \implies z = 0 |
\int \left(1\right) dx = x + C |
a \left(6 + a\right) = 6 a + a^2 |
\frac{-44}{23} = \frac{-44}{23} |
4 + b = 0 \implies b = -4 |
f(y) = 3 + 3 y + y^2, \quad g(a) = 2 + a \implies f(g(a)) = 13 + 7 a + a^2 |
u^2 \left(4 - x\right) = -u^2 x + 4 u^2 |
\frac{-34}{11} = \frac{-34}{11} |
\log_{3}\left(3 + 3 w\right) = 2 \implies w = 2 |
\frac{d}{dz}\left(z^4\right) = 4 z^3 |
\log_{2}\left(7 + 4 c\right) = 3 \implies c = \frac{1}{4} |
\left(t + u\right) \cos{\left(u\right)} = t \cos{\left(u\right)} + u \cos{\left(u\right)} |
f(z) = 1 + 5 z + z^2, \quad g(y) = 1 + 2 y \implies f(g(y)) = 7 + 14 y + 4 y^2 |
8 + v = 0 \implies v = -8 |
(1, -4, 4) \times (4, 3, 2) = (-20, 14, 19) |
11 - 30 = -19 |
-17 + 17 = 0 |
\frac{d}{dw}\left(\cos{\left(w\right)}\right) = -\sin{\left(w\right)} |
\lim_{w \to -3} \left(w\right) = -3 |
\log_{5}\left(4 + 3 w\right) = 3 \implies w = \frac{121}{3} |
-40 - 3 c + c^2 = 0 \implies c \in \{ -5, 8 \} |
3 \left(-a + w\right) w = -3 a w + 3 w^2 |
\log_{4}\left(2 + 4 u\right) = 2 \implies u = \frac{7}{2} |
32 \cdot 17 = 544 |
13 \cdot 17 = 221 |
-12 - 4 y + 3 y^2 + y^3 = 0 \implies y \in \{ -3, -2, 2 \} |
\log_{5}\left(8 + u\right) = 3 \implies u = 117 |
(3, 3, -5) \times (4, -5, 1) = (-22, -23, -27) |
\int \left(1\right) dz = z + C |
f(x) = 4 + 2 x + x^2, \quad g(u) = 2 + 3 u \implies f(g(u)) = 12 + 18 u + 9 u^2 |
\lim_{a \to -5} \left(-6 + a\right) = -11 |
f(z) = 5 + 2 z + z^2, \quad g(a) = 2 + 3 a \implies f(g(a)) = 13 + 18 a + 9 a^2 |
10 + 1 = 11 |
f(c) = 2 + 3 c + c^2, \quad g(z) = 4 + z \implies f(g(z)) = 30 + 11 z + z^2 |
\frac{d}{dt}\left(t^4\right) = 4 t^3 |
\frac{d}{dt}\left(8 + t + t^3\right) = 1 + 3 t^2 |
18 \cdot 8 = 144 |
24 - 10 u + u^2 = 0 \implies u \in \{ 4, 6 \} |
\log_{3}\left(7 + 3 a\right) = 3 \implies a = \frac{20}{3} |
21 \cdot 47 = 987 |
\lim_{x \to 5} \left(x^2\right) = 25 |
7 u + u^2 = 0 \implies u \in \{ -7, 0 \} |
(-5, 5, -3) \times (3, 2, -5) = (-19, -34, -25) |
-4 - 34 = -38 |
\lim_{y \to -2} \left(y\right) = -2 |
48 - 46 a - 3 a^2 + a^3 = 0 \implies a \in \{ -6, 1, 8 \} |
\log_{5}\left(2 + 3 v\right) = 3 \implies v = 41 |
f(b) = 5 + b + b^2, \quad g(t) = 1 + 3 t \implies f(g(t)) = 7 + 9 t + 9 t^2 |
16 - 10 y + y^2 = 0 \implies y \in \{ 2, 8 \} |
-31 - 24 = -55 |
-280 - 19 t + 10 t^2 + t^3 = 0 \implies t \in \{ -8, -7, 5 \} |
40 y - 13 y^2 + y^3 = 0 \implies y \in \{ 0, 5, 8 \} |
\log_{4}\left(7 + v\right) = 2 \implies v = 9 |
f(c) = 2 + 5 c + c^2, \quad g(t) = 1 + 3 t \implies f(g(t)) = 8 + 21 t + 9 t^2 |
\lim_{v \to 0} \left(v\right) = 0 |
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