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\log_{5}\left(1 + a\right) = 3 \implies a = 124 |
-37 \cdot 16 = -592 |
\log_{2}\left(8 + 2 v\right) = 1 \implies v = -3 |
6 - 15 = -9 |
f(t) = 1 + 4 t + t^2, \quad g(z) = 1 + 3 z \implies f(g(z)) = 6 + 18 z + 9 z^2 |
\frac{10}{14} = \frac{5}{7} |
\frac{d}{da}\left(\cos{\left(a\right)}\right) = -\sin{\left(a\right)} |
u^3 \left(u - z\right) = -u^3 z + u^4 |
(3, -2, -4) \times (-1, 3, -5) = (22, 19, 7) |
(0, -1, -3) \times (4, -2, 1) = (-7, -12, 4) |
\frac{d}{dw}\left(\cos{\left(w\right)}\right) = -\sin{\left(w\right)} |
\lim_{a \to 5} \left(a\right) = 5 |
\int \left(3 - 2 x\right) dx = x \left(3 - x\right) + C |
f(z) = 2 + z + z^2, \quad g(b) = 1 + b \implies f(g(b)) = 4 + 3 b + b^2 |
\frac{d}{du}\left(\sin{\left(u\right)}\right) = \cos{\left(u\right)} |
f(u) = 1 + 4 u + u^2, \quad g(y) = 2 + 3 y \implies f(g(y)) = 13 + 24 y + 9 y^2 |
\log_{4}\left(8 + 3 t\right) = 1 \implies t = \frac{-4}{3} |
-64 + c^2 = 0 \implies c \in \{ -8, 8 \} |
-7 - 6 v + v^2 = 0 \implies v \in \{ -1, 7 \} |
21 - 10 u + u^2 = 0 \implies u \in \{ 3, 7 \} |
(1, 1, -2) \times (-4, 1, -5) = (-3, 13, 5) |
-48 + 6 = -42 |
-29 + 3 = -26 |
\int \left(3 y^2 + \sin{\left(y\right)}\right) dy = 1 + y^3 - \cos{\left(y\right)} + C |
\frac{d}{dc}\left(-2 + c + c^2\right) = 1 + 2 c |
-3 + b = 0 \implies b = 3 |
\int \left(2 + \sin{\left(x\right)}\right) dx = 1 + 2 x - \cos{\left(x\right)} + C |
\log_{4}\left(2 + 2 x\right) = 2 \implies x = 7 |
-25 + 25 = 0 |
\lim_{u \to 2} \left(u\right) = 2 |
f(x) = 2 + 5 x + x^2, \quad g(b) = 2 + 3 b \implies f(g(b)) = 16 + 27 b + 9 b^2 |
33 - 44 = -11 |
-144 - 36 c + 4 c^2 + c^3 = 0 \implies c \in \{ -6, -4, 6 \} |
f(a) = 4 + 3 a + a^2, \quad g(w) = 2 + w \implies f(g(w)) = 14 + 7 w + w^2 |
f(t) = 2 + 3 t + t^2, \quad g(v) = 2 + 3 v \implies f(g(v)) = 12 + 21 v + 9 v^2 |
-24 + 2 v + v^2 = 0 \implies v \in \{ -6, 4 \} |
\log_{3}\left(5 + 2 c\right) = 2 \implies c = 2 |
-4 + w = 0 \implies w = 4 |
f(u) = 1 + 2 u + u^2, \quad g(x) = 1 + x \implies f(g(x)) = 4 + 4 x + x^2 |
f(x) = 4 + x + x^2, \quad g(u) = 3 + 2 u \implies f(g(u)) = 16 + 14 u + 4 u^2 |
f(z) = 3 + 3 z + z^2, \quad g(b) = 4 + 3 b \implies f(g(b)) = 31 + 33 b + 9 b^2 |
-150 - 25 a + 6 a^2 + a^3 = 0 \implies a \in \{ -6, -5, 5 \} |
\int \left(1 + 4 c^3\right) dc = c + c^4 + C |
43 + 27 = 70 |
\int \left(-7 + \sin{\left(z\right)}\right) dz = 1 - 7 z - \cos{\left(z\right)} + C |
(2, 4, 4) \times (5, 3, 1) = (-8, 18, -14) |
(-2, 4, -3) \times (0, -1, 2) = (5, 4, 2) |
4 + c = 0 \implies c = -4 |
-2 - w + 2 w^2 + w^3 = 0 \implies w \in \{ -2, -1, 1 \} |
\int \left(-1\right) da = -a + C |
6 + 44 = 50 |
b = 0 \implies b = 0 |
25 - 27 = -2 |
(-1, 4, -1) \times (-4, -4, 5) = (16, 9, 20) |
224 - 60 y - 3 y^2 + y^3 = 0 \implies y \in \{ -8, 4, 7 \} |
\log_{4}\left(1 + 4 u\right) = 2 \implies u = \frac{15}{4} |
-4 + x = 0 \implies x = 4 |
\frac{-26}{32} = \frac{-13}{16} |
\left(9 + z\right) \left(-9 + u\right) = -81 + 9 u - 9 z + u z |
\frac{-27}{4} = \frac{-27}{4} |
15 + 50 = 65 |
\int \left(16\right) dt = 16 t + C |
\int \left(1 + 2 v\right) dv = v + v^2 + C |
\frac{-5}{39} = \frac{-5}{39} |
(3, -5, 0) \times (5, -1, -4) = (20, 12, 22) |
w^3 \left(u + w\right) = u w^3 + w^4 |
41 - 47 = -6 |
24 - 22 w - 3 w^2 + w^3 = 0 \implies w \in \{ -4, 1, 6 \} |
\lim_{c \to 0} \left(c\right) = 0 |
\lim_{u \to 5} \left(-u\right) = -5 |
-10 + 3 a + a^2 = 0 \implies a \in \{ -5, 2 \} |
\int \left(1 + 2 v\right) dv = v + v^2 + C |
f(z) = 1 + 5 z + z^2, \quad g(t) = 2 + 2 t \implies f(g(t)) = 15 + 18 t + 4 t^2 |
f(v) = 4 + 5 v + v^2, \quad g(u) = 3 + 3 u \implies f(g(u)) = 28 + 33 u + 9 u^2 |
\lim_{y \to 3} \left(-2 + y\right) = 1 |
\left(a + w\right) \left(9 - a\right) = 9 a + 9 w - a w - a^2 |
5 + y = 0 \implies y = -5 |
\log_{5}\left(3 + 3 a\right) = 2 \implies a = \frac{22}{3} |
20 + 9 t + t^2 = 0 \implies t \in \{ -5, -4 \} |
\log_{2}\left(8 + c\right) = 2 \implies c = -4 |
\lim_{t \to 4} \left(2 t\right) = 8 |
u = 0 \implies u = 0 |
f(t) = 4 + 2 t + t^2, \quad g(v) = 2 + 2 v \implies f(g(v)) = 12 + 12 v + 4 v^2 |
112 - 16 a - 7 a^2 + a^3 = 0 \implies a \in \{ -4, 4, 7 \} |
7 + z = 0 \implies z = -7 |
6 + 7 y + y^2 = 0 \implies y \in \{ -6, -1 \} |
-43 + 5 = -38 |
f(a) = 4 + 2 a + a^2, \quad g(v) = 3 + v \implies f(g(v)) = 19 + 8 v + v^2 |
f(z) = 3 + 5 z + z^2, \quad g(b) = 1 + 3 b \implies f(g(b)) = 9 + 21 b + 9 b^2 |
\log_{2}\left(3 + c\right) = 1 \implies c = -1 |
1 + b = 0 \implies b = -1 |
\lim_{t \to 0} \left(t\right) = 0 |
b \left(9 + b\right) = 9 b + b^2 |
f(t) = 5 + 3 t + t^2, \quad g(c) = 3 + 3 c \implies f(g(c)) = 23 + 27 c + 9 c^2 |
16 + 10 b + b^2 = 0 \implies b \in \{ -8, -2 \} |
-96 - 52 u + u^3 = 0 \implies u \in \{ -6, -2, 8 \} |
5 + t = 0 \implies t = -5 |
f(a) = 2 + 5 a + a^2, \quad g(w) = 1 + w \implies f(g(w)) = 8 + 7 w + w^2 |
\frac{d}{dz}\left(z\right) = 1 |
f(x) = 5 + 3 x + x^2, \quad g(a) = 3 + 3 a \implies f(g(a)) = 23 + 27 a + 9 a^2 |
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