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\int \left(2 a\right) da = a^2 + C |
f(t) = 4 + 5 t + t^2, \quad g(z) = 4 + z \implies f(g(z)) = 40 + 13 z + z^2 |
f(x) = 2 + 3 x + x^2, \quad g(t) = 3 + t \implies f(g(t)) = 20 + 9 t + t^2 |
f(z) = 3 + 2 z + z^2, \quad g(a) = 1 + a \implies f(g(a)) = 6 + 4 a + a^2 |
\lim_{v \to 3} \left(v\right) = 3 |
f(z) = 4 + 4 z + z^2, \quad g(x) = 4 + 2 x \implies f(g(x)) = 36 + 24 x + 4 x^2 |
\left(-7 + x\right)^2 = 49 - 14 x + x^2 |
\frac{d}{dv}\left(-2 v + \sin{\left(v\right)}\right) = -2 + \cos{\left(v\right)} |
\log_{2}\left(4 + 2 t\right) = 2 \implies t = 0 |
-33 + 17 = -16 |
60 + 47 z + 12 z^2 + z^3 = 0 \implies z \in \{ -5, -4, -3 \} |
\frac{50}{29} = \frac{50}{29} |
-41 + 37 = -4 |
\frac{d}{dw}\left(w - \cos{\left(w\right)}\right) = 1 + \sin{\left(w\right)} |
14 + 9 b + b^2 = 0 \implies b \in \{ -7, -2 \} |
\frac{20}{4} = 5 |
\log_{2}\left(6 + 3 w\right) = 3 \implies w = \frac{2}{3} |
f(u) = 4 + 3 u + u^2, \quad g(y) = 2 + 2 y \implies f(g(y)) = 14 + 14 y + 4 y^2 |
b \left(9 + b\right) = 9 b + b^2 |
-45 - 4 = -49 |
-50 + 8 = -42 |
(-3, 3, 3) \times (-2, 5, 0) = (-15, -6, -9) |
-96 - 52 v + v^3 = 0 \implies v \in \{ -6, -2, 8 \} |
-19 - 2 = -21 |
f(c) = 3 + 5 c + c^2, \quad g(x) = 2 + 2 x \implies f(g(x)) = 17 + 18 x + 4 x^2 |
18 - 12 = 6 |
-18 \cdot 32 = -576 |
\frac{d}{db}\left(-b^2 + \sin{\left(b\right)}\right) = -2 b + \cos{\left(b\right)} |
-8 \cdot 40 = -320 |
f(w) = 4 + w + w^2, \quad g(t) = 4 + t \implies f(g(t)) = 24 + 9 t + t^2 |
\frac{-28}{46} = \frac{-14}{23} |
\int \left(-\sin{\left(b\right)}\right) db = -1 + \cos{\left(b\right)} + C |
\lim_{w \to -5} \left(\cos{\left(w\right)}\right) = \cos{\left(5\right)} |
\log_{3}\left(7 + 3 x\right) = 2 \implies x = \frac{2}{3} |
\lim_{b \to -4} \left(-2\right) = -2 |
6 + 11 a + 6 a^2 + a^3 = 0 \implies a \in \{ -3, -2, -1 \} |
-7 + y = 0 \implies y = 7 |
\log_{3}\left(4 + 4 v\right) = 1 \implies v = \frac{-1}{4} |
\lim_{x \to 3} \left(5 + x\right) = 8 |
\frac{15}{32} = \frac{15}{32} |
\log_{4}\left(6 + 2 u\right) = 1 \implies u = -1 |
10 + 34 = 44 |
\lim_{x \to 5} \left(x^3\right) = 125 |
c \left(2 + c\right) = 2 c + c^2 |
\frac{-16}{28} = \frac{-4}{7} |
-2 + b = 0 \implies b = 2 |
\lim_{v \to -5} \left(v^3\right) = -125 |
-45 - 2 = -47 |
\int \left(-\sin{\left(b\right)}\right) db = -1 + \cos{\left(b\right)} + C |
f(a) = 2 + 2 a + a^2, \quad g(v) = 1 + v \implies f(g(v)) = 5 + 4 v + v^2 |
(3, 0, 1) \times (5, 5, 0) = (-5, 5, 15) |
\log_{2}\left(4 + 3 c\right) = 3 \implies c = \frac{4}{3} |
(-5, 1, -4) \times (4, -2, -1) = (-9, -21, 6) |
4 + w = 0 \implies w = -4 |
\log_{4}\left(7 + 2 b\right) = 3 \implies b = \frac{57}{2} |
f(t) = 2 + 5 t + t^2, \quad g(v) = 4 + 2 v \implies f(g(v)) = 38 + 26 v + 4 v^2 |
60 - 32 t - t^2 + t^3 = 0 \implies t \in \{ -6, 2, 5 \} |
90 - 3 y - 8 y^2 + y^3 = 0 \implies y \in \{ -3, 5, 6 \} |
f(y) = 4 + 5 y + y^2, \quad g(b) = 1 + 2 b \implies f(g(b)) = 10 + 14 b + 4 b^2 |
(-2, -3, 4) \times (-1, 2, -3) = (1, -10, -7) |
f(c) = 2 + 5 c + c^2, \quad g(w) = 2 + 3 w \implies f(g(w)) = 16 + 27 w + 9 w^2 |
t \left(5 + u\right) = 5 t + t u |
f(w) = 5 + 5 w + w^2, \quad g(b) = 2 + 3 b \implies f(g(b)) = 19 + 27 b + 9 b^2 |
(-4, -4, 0) \times (-2, 0, 5) = (-20, 20, -8) |
\log_{4}\left(4 + 2 c\right) = 3 \implies c = 30 |
4 + v = 0 \implies v = -4 |
\lim_{y \to 3} \left(y^2\right) = 9 |
\left(a + v\right) \left(8 + a\right) = 8 a + 8 v + a v + a^2 |
-36 + z^2 = 0 \implies z \in \{ -6, 6 \} |
8 + v = 0 \implies v = -8 |
\frac{d}{db}\left(\sin{\left(b\right)}\right) = \cos{\left(b\right)} |
(0, -1, -4) \times (1, 4, -1) = (17, -4, 1) |
3 + u = 0 \implies u = -3 |
\left(u - z\right) \left(-5 + u\right) = -5 u + 5 z - u z + u^2 |
126 + 3 t - 10 t^2 + t^3 = 0 \implies t \in \{ -3, 6, 7 \} |
-6 + x = 0 \implies x = 6 |
f(b) = 5 + b + b^2, \quad g(v) = 4 + v \implies f(g(v)) = 25 + 9 v + v^2 |
\frac{-50}{8} = \frac{-25}{4} |
\int \left(2 v\right) dv = v^2 + C |
\cos{\left(t\right)} \left(-7 + t\right) = t \cos{\left(t\right)} - 7 \cos{\left(t\right)} |
(-3, -1, -2) \times (-1, -5, -1) = (-9, -1, 14) |
\log_{5}\left(6 + 2 x\right) = 3 \implies x = \frac{119}{2} |
\frac{d}{dt}\left(-2 t\right) = -2 |
\log_{3}\left(8 + 2 u\right) = 1 \implies u = \frac{-5}{2} |
5 + x = 0 \implies x = -5 |
(0, -3, 1) \times (-1, 5, -4) = (7, -1, -3) |
10 - 13 c + 2 c^2 + c^3 = 0 \implies c \in \{ -5, 1, 2 \} |
2 + x = 0 \implies x = -2 |
\log_{4}\left(4 + 4 w\right) = 1 \implies w = 0 |
\int \left(-\sin{\left(y\right)}\right) dy = -1 + \cos{\left(y\right)} + C |
21 + 1 = 22 |
(2, -4, 4) \times (-3, -4, -1) = (20, -10, -20) |
f(x) = 5 + x + x^2, \quad g(a) = 2 + a \implies f(g(a)) = 11 + 5 a + a^2 |
24 + 11 x + x^2 = 0 \implies x \in \{ -8, -3 \} |
19 \cdot 33 = 627 |
(-1, -1, -3) \times (-2, 4, 1) = (11, 7, -6) |
f(a) = 2 + 5 a + a^2, \quad g(y) = 2 + 3 y \implies f(g(y)) = 16 + 27 y + 9 y^2 |
\frac{d}{dt}\left(2 t^2\right) = 4 t |
\log_{5}\left(6 + 4 b\right) = 3 \implies b = \frac{119}{4} |
\frac{d}{dw}\left(\sin{\left(w\right)}\right) = \cos{\left(w\right)} |
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