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f(y) = 3 + 5 y + y^2, \quad g(x) = 3 + 2 x \implies f(g(x)) = 27 + 22 x + 4 x^2 |
-41 + 10 = -31 |
\log_{5}\left(5 + 2 a\right) = 2 \implies a = 10 |
-7 + u = 0 \implies u = 7 |
12 - 7 y + y^2 = 0 \implies y \in \{ 3, 4 \} |
\lim_{v \to 4} \left(v^3\right) = 64 |
\log_{4}\left(2 + 3 u\right) = 1 \implies u = \frac{2}{3} |
-42 + 41 v - 12 v^2 + v^3 = 0 \implies v \in \{ 2, 3, 7 \} |
\lim_{w \to 2} \left(w^4\right) = 16 |
\left(-u + v\right) \left(5 + u\right) = -5 u + 5 v + u v - u^2 |
v \left(-4 + v\right) = -4 v + v^2 |
\left(9 + w\right) \left(-3 - t\right) = -27 - 9 t - 3 w - t w |
8 \cdot 13 = 104 |
-4 + c = 0 \implies c = 4 |
\frac{10}{18} = \frac{5}{9} |
-70 - 39 u + u^3 = 0 \implies u \in \{ -5, -2, 7 \} |
\log_{2}\left(5 + 3 x\right) = 1 \implies x = -1 |
48 - 17 = 31 |
f(u) = 2 + 4 u + u^2, \quad g(w) = 1 + w \implies f(g(w)) = 7 + 6 w + w^2 |
\log_{4}\left(2 + 2 w\right) = 1 \implies w = 1 |
\log_{5}\left(3 + 4 w\right) = 2 \implies w = \frac{11}{2} |
\log_{3}\left(2 + 4 c\right) = 3 \implies c = \frac{25}{4} |
1 + u = 0 \implies u = -1 |
\frac{d}{dx}\left(x^4\right) = 4 x^3 |
(-1, -3, 3) \times (-1, 1, 4) = (-15, 1, -4) |
12 \cdot 13 = 156 |
48 \cdot 14 = 672 |
\log_{2}\left(4 + 4 x\right) = 3 \implies x = 1 |
\int \left(\cos{\left(x\right)}\right) dx = \sin{\left(x\right)} + C |
(4, 2, -4) \times (-4, -5, -1) = (-22, 20, -12) |
-4 \cdot 30 = -120 |
-3 + x = 0 \implies x = 3 |
-12 - 11 t + 2 t^2 + t^3 = 0 \implies t \in \{ -4, -1, 3 \} |
8 - 47 = -39 |
\frac{35}{43} = \frac{35}{43} |
6 + z = 0 \implies z = -6 |
f(w) = 5 + 3 w + w^2, \quad g(z) = 1 + 2 z \implies f(g(z)) = 9 + 10 z + 4 z^2 |
-35 + 47 c - 13 c^2 + c^3 = 0 \implies c \in \{ 1, 5, 7 \} |
\log_{4}\left(7 + x\right) = 3 \implies x = 57 |
\lim_{v \to 2} \left(-2 v\right) = -4 |
-40 - 25 = -65 |
\int \left(4 z^3 \left(4 - z\right) - z^4\right) dz = z^4 \left(4 - z\right) + C |
-224 - 52 x + 5 x^2 + x^3 = 0 \implies x \in \{ -8, -4, 7 \} |
\int \left(\cos{\left(t\right)}\right) dt = \sin{\left(t\right)} + C |
\log_{2}\left(5 + 3 z\right) = 2 \implies z = \frac{-1}{3} |
\frac{-42}{28} = \frac{-3}{2} |
f(t) = 3 + t + t^2, \quad g(x) = 4 + 3 x \implies f(g(x)) = 23 + 27 x + 9 x^2 |
\frac{d}{dv}\left(\sin{\left(v\right)}\right) = \cos{\left(v\right)} |
f(c) = 4 + 4 c + c^2, \quad g(a) = 3 + 3 a \implies f(g(a)) = 25 + 30 a + 9 a^2 |
f(u) = 4 + 2 u + u^2, \quad g(x) = 4 + 3 x \implies f(g(x)) = 28 + 30 x + 9 x^2 |
17 - 7 = 10 |
f(v) = 1 + 3 v + v^2, \quad g(u) = 2 + u \implies f(g(u)) = 11 + 7 u + u^2 |
\frac{d}{dy}\left(0\right) = 0 |
f(z) = 5 + 4 z + z^2, \quad g(t) = 3 + 3 t \implies f(g(t)) = 26 + 30 t + 9 t^2 |
\frac{9}{44} = \frac{9}{44} |
-15 + 2 v + v^2 = 0 \implies v \in \{ -5, 3 \} |
\int \left(1\right) dw = w + C |
\int \left(1\right) dv = v + C |
f(v) = 5 + 4 v + v^2, \quad g(z) = 4 + z \implies f(g(z)) = 37 + 12 z + z^2 |
-27 \cdot 35 = -945 |
\frac{-23}{32} = \frac{-23}{32} |
\frac{-15}{32} = \frac{-15}{32} |
-14 - 5 x + x^2 = 0 \implies x \in \{ -2, 7 \} |
3 + v = 0 \implies v = -3 |
\log_{2}\left(3 + 2 x\right) = 3 \implies x = \frac{5}{2} |
\lim_{b \to 2} \left(0\right) = 0 |
-3 + c = 0 \implies c = 3 |
f(t) = 3 + t + t^2, \quad g(a) = 1 + 3 a \implies f(g(a)) = 5 + 9 a + 9 a^2 |
-14 \cdot 18 = -252 |
\frac{2}{16} = \frac{1}{8} |
f(x) = 2 + 4 x + x^2, \quad g(u) = 1 + u \implies f(g(u)) = 7 + 6 u + u^2 |
\frac{d}{dz}\left(-6 - z + z^3\right) = -1 + 3 z^2 |
f(u) = 3 + 4 u + u^2, \quad g(w) = 4 + 2 w \implies f(g(w)) = 35 + 24 w + 4 w^2 |
\int \left(\cos{\left(w\right)}\right) dw = \sin{\left(w\right)} + C |
\log_{2}\left(5 + 2 a\right) = 1 \implies a = \frac{-3}{2} |
\int \left(1\right) dy = y + C |
\lim_{w \to -2} \left(\sin{\left(w\right)}\right) = -\sin{\left(2\right)} |
\frac{d}{dc}\left(c^4\right) = 4 c^3 |
\lim_{b \to -5} \left(b\right) = -5 |
\frac{d}{dt}\left(0\right) = 0 |
(3, 5, 2) \times (-4, -5, -4) = (-10, 4, 5) |
(0, -4, 3) \times (-5, -3, 0) = (9, -15, -20) |
50 \cdot 40 = 2000 |
\frac{-22}{50} = \frac{-11}{25} |
30 - 11 z + z^2 = 0 \implies z \in \{ 5, 6 \} |
-84 - 19 u + 6 u^2 + u^3 = 0 \implies u \in \{ -7, -3, 4 \} |
f(u) = 4 + 5 u + u^2, \quad g(w) = 3 + 2 w \implies f(g(w)) = 28 + 22 w + 4 w^2 |
\log_{4}\left(6 + 2 w\right) = 1 \implies w = -1 |
40 - 30 = 10 |
8 + 6 a + a^2 = 0 \implies a \in \{ -4, -2 \} |
f(z) = 3 + 4 z + z^2, \quad g(x) = 4 + 2 x \implies f(g(x)) = 35 + 24 x + 4 x^2 |
5 - 45 = -40 |
3 a + 4 a^2 + a^3 = 0 \implies a \in \{ -3, -1, 0 \} |
\log_{5}\left(2 + 3 w\right) = 1 \implies w = 1 |
9 + 31 = 40 |
\lim_{b \to 0} \left(b\right) = 0 |
(-2, 2, 3) \times (5, -3, 4) = (17, 23, -4) |
32 + 12 b + b^2 = 0 \implies b \in \{ -8, -4 \} |
8 + 2 y - 5 y^2 + y^3 = 0 \implies y \in \{ -1, 2, 4 \} |
\frac{d}{dw}\left(0\right) = 0 |
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