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f(b) = 2 + 5 b + b^2, \quad g(z) = 3 + 2 z \implies f(g(z)) = 26 + 22 z + 4 z^2 |
\int \left(\cos{\left(b\right)}\right) db = \sin{\left(b\right)} + C |
\frac{d}{da}\left(a \left(-8 + a\right)\right) = -8 + 2 a |
\log_{3}\left(2 + 2 a\right) = 3 \implies a = \frac{25}{2} |
-36 - 15 = -51 |
\lim_{y \to 5} \left(9 + y\right) = 14 |
\log_{4}\left(6 + 3 z\right) = 1 \implies z = \frac{-2}{3} |
(-3, 5, 1) \times (-1, 3, -3) = (-18, -10, -4) |
\log_{2}\left(7 + w\right) = 1 \implies w = -5 |
\frac{d}{du}\left(u^3 + \cos{\left(u\right)}\right) = 3 u^2 - \sin{\left(u\right)} |
f(w) = 2 + 2 w + w^2, \quad g(x) = 1 + 2 x \implies f(g(x)) = 5 + 8 x + 4 x^2 |
\log_{2}\left(1 + 2 v\right) = 1 \implies v = \frac{1}{2} |
(0, 0, 4) \times (-3, -1, 0) = (4, -12, 0) |
16 - 10 z + z^2 = 0 \implies z \in \{ 2, 8 \} |
6 + y = 0 \implies y = -6 |
f(u) = 5 + 3 u + u^2, \quad g(t) = 2 + 2 t \implies f(g(t)) = 15 + 14 t + 4 t^2 |
\int \left(-7\right) dv = -7 v + C |
f(a) = 3 + 5 a + a^2, \quad g(y) = 2 + y \implies f(g(y)) = 17 + 9 y + y^2 |
(-2, -5, 2) \times (-2, -5, 1) = (5, -2, 0) |
31 \cdot 30 = 930 |
\frac{d}{dw}\left(0\right) = 0 |
-27 \cdot 41 = -1107 |
-20 - 4 c + 5 c^2 + c^3 = 0 \implies c \in \{ -5, -2, 2 \} |
\frac{d}{du}\left(u^5\right) = 5 u^4 |
\log_{5}\left(1 + 2 c\right) = 3 \implies c = 62 |
u y \left(u + y\right) = u y^2 + u^2 y |
18 + 9 a + a^2 = 0 \implies a \in \{ -6, -3 \} |
f(u) = 5 + 2 u + u^2, \quad g(t) = 1 + 2 t \implies f(g(t)) = 8 + 8 t + 4 t^2 |
-15 + 23 x - 9 x^2 + x^3 = 0 \implies x \in \{ 1, 3, 5 \} |
f(b) = 2 + 4 b + b^2, \quad g(x) = 2 + 2 x \implies f(g(x)) = 14 + 16 x + 4 x^2 |
64 - 24 a - 6 a^2 + a^3 = 0 \implies a \in \{ -4, 2, 8 \} |
f(z) = 3 + 5 z + z^2, \quad g(u) = 4 + 3 u \implies f(g(u)) = 39 + 39 u + 9 u^2 |
f(a) = 1 + 3 a + a^2, \quad g(t) = 2 + 2 t \implies f(g(t)) = 11 + 14 t + 4 t^2 |
f(w) = 1 + 2 w + w^2, \quad g(c) = 2 + c \implies f(g(c)) = 9 + 6 c + c^2 |
\frac{-3}{27} = \frac{-1}{9} |
\lim_{z \to -1} \left(\sin{\left(z\right)}\right) = -\sin{\left(1\right)} |
\lim_{b \to -2} \left(\cos{\left(b\right)}\right) = \cos{\left(2\right)} |
f(c) = 5 + c + c^2, \quad g(t) = 1 + 2 t \implies f(g(t)) = 7 + 6 t + 4 t^2 |
\frac{d}{dx}\left(-7 x\right) = -7 |
\log_{5}\left(8 + 3 x\right) = 2 \implies x = \frac{17}{3} |
-24 + 2 x + x^2 = 0 \implies x \in \{ -6, 4 \} |
10 \left(8 - w\right) = 80 - 10 w |
\log_{2}\left(8 + v\right) = 2 \implies v = -4 |
\int \left(1\right) dv = v + C |
f(t) = 1 + 4 t + t^2, \quad g(c) = 3 + 2 c \implies f(g(c)) = 22 + 20 c + 4 c^2 |
\frac{d}{dy}\left(y\right) = 1 |
\frac{d}{dx}\left(2 x - \left(-7 + x\right)\right) = 1 |
\log_{4}\left(8 + 3 c\right) = 2 \implies c = \frac{8}{3} |
\int \left(4 w^3\right) dw = w^4 + C |
4 + v = 0 \implies v = -4 |
43 \cdot 8 = 344 |
\lim_{w \to -4} \left(w\right) = -4 |
\log_{5}\left(3 + 4 u\right) = 1 \implies u = \frac{1}{2} |
2 + b = 0 \implies b = -2 |
-6 + 20 = 14 |
-5 u + u^2 = 0 \implies u \in \{ 0, 5 \} |
\log_{5}\left(8 + t\right) = 3 \implies t = 117 |
2 v \left(7 + x\right) = 14 v + 2 v x |
f(u) = 5 + 2 u + u^2, \quad g(a) = 4 + 3 a \implies f(g(a)) = 29 + 30 a + 9 a^2 |
-21 - 4 w + w^2 = 0 \implies w \in \{ -3, 7 \} |
f(y) = 4 + y + y^2, \quad g(a) = 4 + 2 a \implies f(g(a)) = 24 + 18 a + 4 a^2 |
\frac{d}{dw}\left(w^2\right) = 2 w |
\lim_{t \to -5} \left(5 + t\right) = 0 |
120 - 31 u - 6 u^2 + u^3 = 0 \implies u \in \{ -5, 3, 8 \} |
\frac{d}{dv}\left(2 v \left(1 + v\right)\right) = 2 v + 2 \left(1 + v\right) |
\log_{2}\left(7 + 3 b\right) = 2 \implies b = -1 |
\log_{5}\left(6 + t\right) = 2 \implies t = 19 |
\frac{20}{29} = \frac{20}{29} |
f(a) = 5 + 3 a + a^2, \quad g(w) = 1 + w \implies f(g(w)) = 9 + 5 w + w^2 |
42 + 55 w + 14 w^2 + w^3 = 0 \implies w \in \{ -7, -6, -1 \} |
\log_{2}\left(6 + 2 z\right) = 1 \implies z = -2 |
\int \left(-2\right) dc = -2 c + C |
\frac{d}{dt}\left(-4\right) = 0 |
(5, 3, 5) \times (-5, -5, 4) = (37, -45, -10) |
\log_{4}\left(8 + 2 z\right) = 3 \implies z = 28 |
f(u) = 1 + 3 u + u^2, \quad g(v) = 4 + 3 v \implies f(g(v)) = 29 + 33 v + 9 v^2 |
\lim_{a \to 3} \left(10 + a\right) = 13 |
\log_{5}\left(8 + 2 x\right) = 1 \implies x = \frac{-3}{2} |
t \left(-3 + a\right) = -3 t + a t |
18 + 4 = 22 |
\int \left(-10 - 2 x\right) dx = -10 x - x^2 + C |
\log_{3}\left(5 + 2 y\right) = 1 \implies y = -1 |
\frac{21}{29} = \frac{21}{29} |
(-4, 5, -1) \times (-1, 4, 3) = (19, 13, -11) |
4 + x = 0 \implies x = -4 |
4 \cdot 43 = 172 |
-5 + 4 v + v^2 = 0 \implies v \in \{ -5, 1 \} |
\log_{3}\left(7 + 2 z\right) = 3 \implies z = 10 |
\int \left(2 + 2 x\right) dx = 2 x + x^2 + C |
\lim_{x \to -5} \left(6 + x\right) = 1 |
f(x) = 3 + x + x^2, \quad g(c) = 4 + 3 c \implies f(g(c)) = 23 + 27 c + 9 c^2 |
56 - 57 x + x^3 = 0 \implies x \in \{ -8, 1, 7 \} |
(2, -3, 2) \times (-3, 5, 4) = (-22, -14, 1) |
\int \left(7 t^6\right) dt = t^7 + C |
7 u \left(-7 + y\right) = -49 u + 7 u y |
\frac{d}{dw}\left(w^3 \cos{\left(w\right)}\right) = 3 w^2 \cos{\left(w\right)} - w^3 \sin{\left(w\right)} |
f(z) = 4 + 4 z + z^2, \quad g(v) = 2 + v \implies f(g(v)) = 16 + 8 v + v^2 |
\frac{d}{dc}\left(c + \sin{\left(c\right)}\right) = 1 + \cos{\left(c\right)} |
\frac{d}{dz}\left(z^4\right) = 4 z^3 |
f(z) = 1 + 4 z + z^2, \quad g(c) = 4 + 3 c \implies f(g(c)) = 33 + 36 c + 9 c^2 |
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