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f(y) = 3 + 5 y + y^2, \quad g(w) = 3 + w \implies f(g(w)) = 27 + 11 w + w^2 |
40 - 22 t - t^2 + t^3 = 0 \implies t \in \{ -5, 2, 4 \} |
\frac{d}{da}\left(a\right) = 1 |
\log_{3}\left(2 + 3 a\right) = 3 \implies a = \frac{25}{3} |
-3 + u = 0 \implies u = 3 |
1 - 9 = -8 |
\frac{d}{dy}\left(\sin{\left(y\right)}\right) = \cos{\left(y\right)} |
\frac{d}{da}\left(\sin{\left(a\right)}\right) = \cos{\left(a\right)} |
8 - 10 t + t^2 + t^3 = 0 \implies t \in \{ -4, 1, 2 \} |
f(c) = 2 + 2 c + c^2, \quad g(z) = 4 + 2 z \implies f(g(z)) = 26 + 20 z + 4 z^2 |
f(w) = 2 + w + w^2, \quad g(u) = 1 + 3 u \implies f(g(u)) = 4 + 9 u + 9 u^2 |
\log_{5}\left(1 + 4 y\right) = 3 \implies y = 31 |
\lim_{x \to 4} \left(\sin{\left(x\right)}\right) = \sin{\left(4\right)} |
-45 \cdot 35 = -1575 |
4 + b = 0 \implies b = -4 |
\frac{24}{38} = \frac{12}{19} |
\lim_{a \to -1} \left(a\right) = -1 |
-64 + a^2 = 0 \implies a \in \{ -8, 8 \} |
\int \left(4 z^3\right) dz = z^4 + C |
\log_{2}\left(3 + 4 t\right) = 3 \implies t = \frac{5}{4} |
31 - 9 = 22 |
x^3 \left(-6 + t\right) = t x^3 - 6 x^3 |
f(x) = 1 + 2 x + x^2, \quad g(v) = 1 + v \implies f(g(v)) = 4 + 4 v + v^2 |
w = 0 \implies w = 0 |
\int \left(\cos{\left(x\right)}\right) dx = \sin{\left(x\right)} + C |
33 + 48 = 81 |
-2 + u = 0 \implies u = 2 |
18 - 9 v + v^2 = 0 \implies v \in \{ 3, 6 \} |
u^4 \left(9 + u\right) = 9 u^4 + u^5 |
\frac{3}{49} = \frac{3}{49} |
\frac{d}{dw}\left(\cos{\left(w\right)}\right) = -\sin{\left(w\right)} |
\int \left(3\right) dv = 3 v + C |
f(b) = 5 + b + b^2, \quad g(w) = 2 + 2 w \implies f(g(w)) = 11 + 10 w + 4 w^2 |
-19 - 13 = -32 |
\int \left(-1 + \sin{\left(t\right)}\right) dt = 1 - t - \cos{\left(t\right)} + C |
\int \left(-2 c \sin{\left(c\right)} + 2 \cos{\left(c\right)}\right) dc = 2 c \cos{\left(c\right)} + C |
15 - 8 a + a^2 = 0 \implies a \in \{ 3, 5 \} |
5 + a = 0 \implies a = -5 |
280 - 51 z - 6 z^2 + z^3 = 0 \implies z \in \{ -7, 5, 8 \} |
20 + 29 x + 10 x^2 + x^3 = 0 \implies x \in \{ -5, -4, -1 \} |
-25 - 5 = -30 |
\frac{-34}{17} = -2 |
15 + 8 v + v^2 = 0 \implies v \in \{ -5, -3 \} |
-4 + y = 0 \implies y = 4 |
\int \left(1\right) dz = z + C |
100 - 25 c - 4 c^2 + c^3 = 0 \implies c \in \{ -5, 4, 5 \} |
\int \left(5 x^4\right) dx = x^5 + C |
(-3, 0, 0) \times (-1, -2, -5) = (0, -15, 6) |
(-3, -1, -1) \times (-3, 4, 4) = (0, 15, -15) |
\left(a + b\right) \sin{\left(a\right)} = a \sin{\left(a\right)} + b \sin{\left(a\right)} |
-280 - 51 t + 6 t^2 + t^3 = 0 \implies t \in \{ -8, -5, 7 \} |
-128 - 16 x + 8 x^2 + x^3 = 0 \implies x \in \{ -8, -4, 4 \} |
-10 + 17 x - 8 x^2 + x^3 = 0 \implies x \in \{ 1, 2, 5 \} |
f(a) = 5 + 3 a + a^2, \quad g(t) = 2 + 3 t \implies f(g(t)) = 15 + 21 t + 9 t^2 |
-35 + 3 = -32 |
(0, -4, -4) \times (2, -3, -3) = (0, -8, 8) |
f(c) = 3 + 5 c + c^2, \quad g(z) = 3 + z \implies f(g(z)) = 27 + 11 z + z^2 |
\frac{20}{41} = \frac{20}{41} |
6 + 5 c + c^2 = 0 \implies c \in \{ -3, -2 \} |
-49 + a^2 = 0 \implies a \in \{ -7, 7 \} |
\frac{41}{25} = \frac{41}{25} |
(4, -2, 3) \times (4, 0, -1) = (2, 16, 8) |
\frac{d}{dv}\left(\sin{\left(v\right)}\right) = \cos{\left(v\right)} |
-40 - 5 = -45 |
f(b) = 5 + 5 b + b^2, \quad g(v) = 4 + 3 v \implies f(g(v)) = 41 + 39 v + 9 v^2 |
f(x) = 4 + 3 x + x^2, \quad g(c) = 4 + 2 c \implies f(g(c)) = 32 + 22 c + 4 c^2 |
(-1, -3, -3) \times (3, 3, 3) = (0, -6, 6) |
\lim_{a \to 3} \left(a^2\right) = 9 |
\int \left(1 - \sin{\left(x\right)}\right) dx = -1 + x + \cos{\left(x\right)} + C |
\log_{2}\left(2 + 2 x\right) = 2 \implies x = 1 |
-28 - 3 t + t^2 = 0 \implies t \in \{ -4, 7 \} |
-32 - 4 v + v^2 = 0 \implies v \in \{ -4, 8 \} |
-4 + a^2 = 0 \implies a \in \{ -2, 2 \} |
80 + 66 x + 15 x^2 + x^3 = 0 \implies x \in \{ -8, -5, -2 \} |
3 + x = 0 \implies x = -3 |
-31 \cdot 26 = -806 |
10 + 18 = 28 |
-14 \cdot 45 = -630 |
f(x) = 5 + 4 x + x^2, \quad g(v) = 2 + v \implies f(g(v)) = 17 + 8 v + v^2 |
6 u + u^2 = 0 \implies u \in \{ -6, 0 \} |
-5 y + y^2 = 0 \implies y \in \{ 0, 5 \} |
\frac{-24}{26} = \frac{-12}{13} |
-8 - 7 = -15 |
f(b) = 3 + 5 b + b^2, \quad g(t) = 1 + 3 t \implies f(g(t)) = 9 + 21 t + 9 t^2 |
\lim_{b \to -5} \left(8 + b\right) = 3 |
\log_{5}\left(8 + z\right) = 1 \implies z = -3 |
\log_{3}\left(1 + 3 z\right) = 1 \implies z = \frac{2}{3} |
2 v \left(5 + v\right) = 10 v + 2 v^2 |
\log_{3}\left(6 + b\right) = 2 \implies b = 3 |
-5 + 42 = 37 |
\frac{d}{dv}\left(-3\right) = 0 |
-40 - 43 x - 2 x^2 + x^3 = 0 \implies x \in \{ -5, -1, 8 \} |
\log_{4}\left(5 + 4 c\right) = 3 \implies c = \frac{59}{4} |
\log_{4}\left(4 + 2 y\right) = 1 \implies y = 0 |
2 + w = 0 \implies w = -2 |
-2 - 13 = -15 |
\sin{\left(u\right)} \left(-5 - u\right) = -u \sin{\left(u\right)} - 5 \sin{\left(u\right)} |
f(t) = 1 + 5 t + t^2, \quad g(a) = 2 + 2 a \implies f(g(a)) = 15 + 18 a + 4 a^2 |
f(w) = 4 + 2 w + w^2, \quad g(z) = 2 + 2 z \implies f(g(z)) = 12 + 12 z + 4 z^2 |
f(z) = 4 + 5 z + z^2, \quad g(y) = 2 + y \implies f(g(y)) = 18 + 9 y + y^2 |
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