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f(u) = 3 + 2 u + u^2, \quad g(v) = 4 + v \implies f(g(v)) = 27 + 10 v + v^2 |
\int \left(4 t^3\right) dt = t^4 + C |
2 \cdot 22 = 44 |
b^4 \left(-5 - z\right) = -b^4 z - 5 b^4 |
\log_{4}\left(8 + 4 v\right) = 1 \implies v = -1 |
\sin{\left(v\right)} \left(-4 + y\right) = y \sin{\left(v\right)} - 4 \sin{\left(v\right)} |
\int \left(2 y\right) dy = y^2 + C |
a^4 \left(1 + a\right) = a^4 + a^5 |
\frac{d}{dx}\left(-5 \left(1 + x\right)\right) = -5 |
\lim_{u \to 1} \left(-4 + u\right) = -3 |
\frac{d}{dy}\left(y^4 \left(-5 - y\right)\right) = 4 y^3 \left(-5 - y\right) - y^4 |
\frac{d}{db}\left(\cos{\left(b\right)}\right) = -\sin{\left(b\right)} |
f(x) = 2 + 2 x + x^2, \quad g(u) = 1 + 3 u \implies f(g(u)) = 5 + 12 u + 9 u^2 |
w^4 \left(-4 + a\right) = a w^4 - 4 w^4 |
\frac{17}{47} = \frac{17}{47} |
2 + v = 0 \implies v = -2 |
27 \cdot 47 = 1269 |
\int \left(3 w^2\right) dw = w^3 + C |
\int \left(3 c^2\right) dc = c^3 + C |
4 \cdot 50 = 200 |
\int \left(2 z\right) dz = z^2 + C |
7 w + w^2 = 0 \implies w \in \{ -7, 0 \} |
13 + 13 = 26 |
\log_{5}\left(2 + 4 c\right) = 3 \implies c = \frac{123}{4} |
f(z) = 1 + 5 z + z^2, \quad g(c) = 3 + c \implies f(g(c)) = 25 + 11 c + c^2 |
-56 - c + c^2 = 0 \implies c \in \{ -7, 8 \} |
-5 \cdot 25 = -125 |
(1, 3, -5) \times (-3, -5, 2) = (-19, 13, 4) |
\int \left(1\right) dw = w + C |
\log_{5}\left(8 + 2 z\right) = 2 \implies z = \frac{17}{2} |
\frac{d}{dz}\left(z^3\right) = 3 z^2 |
6 + 7 z + z^2 = 0 \implies z \in \{ -6, -1 \} |
7 + t = 0 \implies t = -7 |
\frac{d}{dz}\left(0\right) = 0 |
-16 - 4 w + 4 w^2 + w^3 = 0 \implies w \in \{ -4, -2, 2 \} |
-16 + b^2 = 0 \implies b \in \{ -4, 4 \} |
\frac{6}{42} = \frac{1}{7} |
-70 - 39 c + c^3 = 0 \implies c \in \{ -5, -2, 7 \} |
\frac{d}{dx}\left(-x + x^2\right) = -1 + 2 x |
7 + v = 0 \implies v = -7 |
-7 + 6 t + t^2 = 0 \implies t \in \{ -7, 1 \} |
120 - 26 v - 5 v^2 + v^3 = 0 \implies v \in \{ -5, 4, 6 \} |
90 - 27 a - 4 a^2 + a^3 = 0 \implies a \in \{ -5, 3, 6 \} |
-60 - 28 t + 3 t^2 + t^3 = 0 \implies t \in \{ -6, -2, 5 \} |
4 a + a^2 = 0 \implies a \in \{ -4, 0 \} |
\lim_{w \to -4} \left(3\right) = 3 |
\int \left(3 w^2\right) dw = w^3 + C |
-14 + 23 z - 10 z^2 + z^3 = 0 \implies z \in \{ 1, 2, 7 \} |
f(v) = 5 + 5 v + v^2, \quad g(z) = 1 + z \implies f(g(z)) = 11 + 7 z + z^2 |
\lim_{t \to 0} \left(2 t\right) = 0 |
-14 + 5 w + w^2 = 0 \implies w \in \{ -7, 2 \} |
\log_{2}\left(3 + 4 a\right) = 1 \implies a = \frac{-1}{4} |
35 + 47 w + 13 w^2 + w^3 = 0 \implies w \in \{ -7, -5, -1 \} |
\int \left(2 + 2 y\right) dy = 2 y + y^2 + C |
\int \left(-1 + 2 b\right) db = -b + b^2 + C |
\log_{2}\left(6 + 4 x\right) = 2 \implies x = \frac{-1}{2} |
\log_{5}\left(3 + 4 y\right) = 3 \implies y = \frac{61}{2} |
f(u) = 1 + 4 u + u^2, \quad g(b) = 1 + b \implies f(g(b)) = 6 + 6 b + b^2 |
\lim_{b \to -3} \left(b^2\right) = 9 |
f(b) = 1 + 3 b + b^2, \quad g(u) = 3 + 2 u \implies f(g(u)) = 19 + 18 u + 4 u^2 |
-60 - 28 w + 3 w^2 + w^3 = 0 \implies w \in \{ -6, -2, 5 \} |
\lim_{x \to 5} \left(1 + x\right) = 6 |
f(t) = 4 + 4 t + t^2, \quad g(a) = 3 + 3 a \implies f(g(a)) = 25 + 30 a + 9 a^2 |
\lim_{b \to -3} \left(\cos{\left(b\right)}\right) = \cos{\left(3\right)} |
\int \left(3 c^2\right) dc = c^3 + C |
f(c) = 5 + 3 c + c^2, \quad g(b) = 1 + 3 b \implies f(g(b)) = 9 + 15 b + 9 b^2 |
-3 + w = 0 \implies w = 3 |
-6 - 5 x + x^2 = 0 \implies x \in \{ -1, 6 \} |
\frac{d}{dx}\left(\sin{\left(x\right)}\right) = \cos{\left(x\right)} |
\frac{d}{dc}\left(c^2\right) = 2 c |
-8 + 5 = -3 |
-4 + u = 0 \implies u = 4 |
(1, 5, 5) \times (-1, -2, -3) = (-5, -2, 3) |
\log_{4}\left(5 + 2 t\right) = 3 \implies t = \frac{59}{2} |
-80 - 16 a + 5 a^2 + a^3 = 0 \implies a \in \{ -5, -4, 4 \} |
\frac{4}{50} = \frac{2}{25} |
f(b) = 1 + 5 b + b^2, \quad g(x) = 4 + 2 x \implies f(g(x)) = 37 + 26 x + 4 x^2 |
\int \left(1\right) db = b + C |
f(x) = 1 + 5 x + x^2, \quad g(a) = 4 + 3 a \implies f(g(a)) = 37 + 39 a + 9 a^2 |
(-5, 2, 5) \times (2, -4, 3) = (26, 25, 16) |
(-5, -2, -5) \times (0, 0, 0) = (0, 0, 0) |
-7 + x = 0 \implies x = 7 |
\log_{5}\left(5 + a\right) = 3 \implies a = 120 |
-8 + a = 0 \implies a = 8 |
\log_{5}\left(4 + 3 c\right) = 3 \implies c = \frac{121}{3} |
f(z) = 3 + 3 z + z^2, \quad g(t) = 3 + t \implies f(g(t)) = 21 + 9 t + t^2 |
6 + b = 0 \implies b = -6 |
f(b) = 1 + 2 b + b^2, \quad g(v) = 3 + v \implies f(g(v)) = 16 + 8 v + v^2 |
-224 - 60 u + 3 u^2 + u^3 = 0 \implies u \in \{ -7, -4, 8 \} |
(4, 5, 1) \times (-3, 0, -5) = (-25, 17, 15) |
(1, 2, 5) \times (-2, 0, 5) = (10, -15, 4) |
f(u) = 3 + 3 u + u^2, \quad g(t) = 3 + 3 t \implies f(g(t)) = 21 + 27 t + 9 t^2 |
\lim_{c \to 0} \left(7 - c\right) = 7 |
-6 + w = 0 \implies w = 6 |
\log_{3}\left(8 + 3 v\right) = 1 \implies v = \frac{-5}{3} |
\frac{-38}{14} = \frac{-19}{7} |
-3 + y = 0 \implies y = 3 |
8 + 6 b + b^2 = 0 \implies b \in \{ -4, -2 \} |
72 + 54 v + 13 v^2 + v^3 = 0 \implies v \in \{ -6, -4, -3 \} |
7 + y = 0 \implies y = -7 |
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