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f(y) = 3 + 2 y + y^2, \quad g(z) = 2 + 3 z \implies f(g(z)) = 11 + 18 z + 9 z^2 |
\int \left(3 w^2 \left(-2 + w\right) + w^3\right) dw = w^3 \left(-2 + w\right) + C |
\log_{4}\left(2 + y\right) = 2 \implies y = 14 |
(-1, 2, -1) \times (0, 3, -5) = (-7, -5, -3) |
\log_{3}\left(6 + 4 v\right) = 1 \implies v = \frac{-3}{4} |
\lim_{u \to -4} \left(u\right) = -4 |
f(x) = 1 + 5 x + x^2, \quad g(y) = 4 + 3 y \implies f(g(y)) = 37 + 39 y + 9 y^2 |
-19 + 41 = 22 |
44 - 36 = 8 |
f(z) = 5 + z + z^2, \quad g(w) = 2 + w \implies f(g(w)) = 11 + 5 w + w^2 |
\int \left(1\right) dy = y + C |
\frac{-29}{11} = \frac{-29}{11} |
f(w) = 2 + 2 w + w^2, \quad g(c) = 2 + 3 c \implies f(g(c)) = 10 + 18 c + 9 c^2 |
f(y) = 1 + 3 y + y^2, \quad g(a) = 2 + 2 a \implies f(g(a)) = 11 + 14 a + 4 a^2 |
5 + c = 0 \implies c = -5 |
\frac{d}{dc}\left(\sin{\left(c\right)}\right) = \cos{\left(c\right)} |
\log_{2}\left(6 + 2 v\right) = 1 \implies v = -2 |
\log_{4}\left(1 + 4 v\right) = 3 \implies v = \frac{63}{4} |
f(b) = 2 + 4 b + b^2, \quad g(v) = 2 + 2 v \implies f(g(v)) = 14 + 16 v + 4 v^2 |
24 - 4 u - 6 u^2 + u^3 = 0 \implies u \in \{ -2, 2, 6 \} |
f(x) = 5 + x + x^2, \quad g(b) = 1 + 3 b \implies f(g(b)) = 7 + 9 b + 9 b^2 |
f(c) = 1 + 2 c + c^2, \quad g(w) = 3 + w \implies f(g(w)) = 16 + 8 w + w^2 |
\log_{4}\left(1 + 4 c\right) = 1 \implies c = \frac{3}{4} |
\frac{-8}{25} = \frac{-8}{25} |
\int \left(1 - 3 w^2\right) dw = w - w^3 + C |
f(u) = 1 + 3 u + u^2, \quad g(c) = 3 + 2 c \implies f(g(c)) = 19 + 18 c + 4 c^2 |
\log_{4}\left(3 + 2 a\right) = 2 \implies a = \frac{13}{2} |
\int \left(-\sin{\left(x\right)}\right) dx = -1 + \cos{\left(x\right)} + C |
\frac{-20}{34} = \frac{-10}{17} |
\int \left(\cos{\left(y\right)}\right) dy = \sin{\left(y\right)} + C |
4 + 5 c + c^2 = 0 \implies c \in \{ -4, -1 \} |
\int \left(2 z \sin{\left(z\right)} + z^2 \cos{\left(z\right)}\right) dz = z^2 \sin{\left(z\right)} + C |
\frac{d}{dt}\left(t\right) = 1 |
\frac{14}{15} = \frac{14}{15} |
16 a - 10 a^2 + a^3 = 0 \implies a \in \{ 0, 2, 8 \} |
\lim_{a \to 1} \left(a^2\right) = 1 |
6 - 7 t + t^2 = 0 \implies t \in \{ 1, 6 \} |
-11 \cdot 38 = -418 |
f(t) = 3 + t + t^2, \quad g(y) = 3 + 2 y \implies f(g(y)) = 15 + 14 y + 4 y^2 |
8 - 6 v - 3 v^2 + v^3 = 0 \implies v \in \{ -2, 1, 4 \} |
(-2, -4, 5) \times (4, -5, 2) = (17, 24, 26) |
\log_{4}\left(3 + 4 u\right) = 3 \implies u = \frac{61}{4} |
(2, -2, -1) \times (-2, -5, 2) = (-9, -2, -14) |
\frac{-23}{2} = \frac{-23}{2} |
-14 - 5 b + b^2 = 0 \implies b \in \{ -2, 7 \} |
-17 \cdot 37 = -629 |
48 + 44 z + 12 z^2 + z^3 = 0 \implies z \in \{ -6, -4, -2 \} |
-33 \cdot 19 = -627 |
\frac{d}{dw}\left(\sin{\left(w\right)}\right) = \cos{\left(w\right)} |
f(x) = 3 + 2 x + x^2, \quad g(y) = 2 + 3 y \implies f(g(y)) = 11 + 18 y + 9 y^2 |
f(t) = 1 + 2 t + t^2, \quad g(z) = 1 + 3 z \implies f(g(z)) = 4 + 12 z + 9 z^2 |
\log_{4}\left(2 + y\right) = 1 \implies y = 2 |
\frac{d}{dx}\left(x^3\right) = 3 x^2 |
17 \cdot 47 = 799 |
\int \left(3 w^2\right) dw = w^3 + C |
\log_{5}\left(4 + 4 b\right) = 3 \implies b = \frac{121}{4} |
14 + 30 = 44 |
(0, 4, 5) \times (-5, 1, -3) = (-17, -25, 20) |
f(u) = 5 + 4 u + u^2, \quad g(a) = 3 + 2 a \implies f(g(a)) = 26 + 20 a + 4 a^2 |
-33 - 27 = -60 |
6 + w = 0 \implies w = -6 |
-19 + 16 = -3 |
\frac{d}{dw}\left(w\right) = 1 |
34 - 22 = 12 |
245 - 49 b - 5 b^2 + b^3 = 0 \implies b \in \{ -7, 5, 7 \} |
f(y) = 3 + 4 y + y^2, \quad g(x) = 4 + 2 x \implies f(g(x)) = 35 + 24 x + 4 x^2 |
44 - 10 = 34 |
-8 + b = 0 \implies b = 8 |
-48 + 46 u - 13 u^2 + u^3 = 0 \implies u \in \{ 2, 3, 8 \} |
8 + z = 0 \implies z = -8 |
-29 \cdot 5 = -145 |
-46 + 3 = -43 |
-23 - 15 = -38 |
36 + 5 = 41 |
\log_{5}\left(1 + 2 u\right) = 1 \implies u = 2 |
\frac{d}{du}\left(\sin{\left(u\right)}\right) = \cos{\left(u\right)} |
26 + 44 = 70 |
\lim_{x \to -4} \left(x^4\right) = 256 |
-4 + b = 0 \implies b = 4 |
(-3, -4, -5) \times (-4, -1, 0) = (-5, 20, -13) |
\log_{2}\left(3 + b\right) = 2 \implies b = 1 |
\frac{d}{db}\left(2 + b\right) = 1 |
(-2, 5, 4) \times (-3, -5, -2) = (10, -16, 25) |
f(w) = 1 + 5 w + w^2, \quad g(u) = 3 + u \implies f(g(u)) = 25 + 11 u + u^2 |
90 - 27 y - 4 y^2 + y^3 = 0 \implies y \in \{ -5, 3, 6 \} |
40 + 13 x + x^2 = 0 \implies x \in \{ -8, -5 \} |
\frac{13}{45} = \frac{13}{45} |
\frac{28}{40} = \frac{7}{10} |
\int \left(3 u^2\right) du = u^3 + C |
\log_{3}\left(5 + 4 y\right) = 1 \implies y = \frac{-1}{2} |
\frac{-13}{40} = \frac{-13}{40} |
-43 \cdot 4 = -172 |
\frac{d}{du}\left(2 u - \left(-10 + u\right)\right) = 1 |
-7 + x = 0 \implies x = 7 |
-60 - 28 v + 3 v^2 + v^3 = 0 \implies v \in \{ -6, -2, 5 \} |
2 + u = 0 \implies u = -2 |
\frac{d}{dz}\left(z^4\right) = 4 z^3 |
-16 + 6 w + w^2 = 0 \implies w \in \{ -8, 2 \} |
\lim_{z \to 2} \left(z^3\right) = 8 |
\frac{d}{dt}\left(t\right) = 1 |
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