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f(t) = 2 + t + t^2, \quad g(b) = 4 + 3 b \implies f(g(b)) = 22 + 27 b + 9 b^2 |
16 - 4 = 12 |
31 \cdot 15 = 465 |
u = 0 \implies u = 0 |
\frac{d}{dw}\left(w^2\right) = 2 w |
24 + 11 t + t^2 = 0 \implies t \in \{ -8, -3 \} |
\int \left(2 x\right) dx = x^2 + C |
-1 + w = 0 \implies w = 1 |
(-3, 4, 5) \times (-3, -2, -1) = (6, -18, 18) |
5 + 6 w + w^2 = 0 \implies w \in \{ -5, -1 \} |
\lim_{u \to 1} \left(u^3\right) = 1 |
2 - 3 t + t^2 = 0 \implies t \in \{ 1, 2 \} |
24 b - 10 b^2 + b^3 = 0 \implies b \in \{ 0, 4, 6 \} |
-18 - 9 y + 2 y^2 + y^3 = 0 \implies y \in \{ -3, -2, 3 \} |
(4, 1, -1) \times (-4, 5, -1) = (4, 8, 24) |
\lim_{y \to 0} \left(8\right) = 8 |
(-3, 2, 5) \times (-5, 2, -3) = (-16, -34, 4) |
\lim_{x \to 5} \left(x^3\right) = 125 |
-48 - 2 c + c^2 = 0 \implies c \in \{ -6, 8 \} |
f(u) = 3 + 2 u + u^2, \quad g(v) = 3 + 3 v \implies f(g(v)) = 18 + 24 v + 9 v^2 |
f(w) = 2 + 5 w + w^2, \quad g(v) = 1 + 2 v \implies f(g(v)) = 8 + 14 v + 4 v^2 |
-4 + z = 0 \implies z = 4 |
f(x) = 1 + 2 x + x^2, \quad g(y) = 2 + y \implies f(g(y)) = 9 + 6 y + y^2 |
f(b) = 2 + 5 b + b^2, \quad g(c) = 4 + c \implies f(g(c)) = 38 + 13 c + c^2 |
-7 + y = 0 \implies y = 7 |
f(y) = 2 + 4 y + y^2, \quad g(t) = 3 + t \implies f(g(t)) = 23 + 10 t + t^2 |
f(u) = 5 + 5 u + u^2, \quad g(b) = 3 + 3 b \implies f(g(b)) = 29 + 33 b + 9 b^2 |
84 - 5 c - 8 c^2 + c^3 = 0 \implies c \in \{ -3, 4, 7 \} |
f(x) = 3 + x + x^2, \quad g(b) = 3 + b \implies f(g(b)) = 15 + 7 b + b^2 |
-28 c + 3 c^2 + c^3 = 0 \implies c \in \{ -7, 0, 4 \} |
\log_{2}\left(8 + 2 w\right) = 3 \implies w = 0 |
\frac{d}{dw}\left(w\right) = 1 |
(-2, 0, -1) \times (3, 4, -2) = (4, -7, -8) |
35 - 27 = 8 |
\frac{d}{dw}\left(\sin{\left(w\right)}\right) = \cos{\left(w\right)} |
(4, 3, 3) \times (-3, 1, 3) = (6, -21, 13) |
\lim_{t \to -5} \left(t^2\right) = 25 |
\int \left(\cos{\left(v\right)}\right) dv = \sin{\left(v\right)} + C |
5 - 6 z + z^2 = 0 \implies z \in \{ 1, 5 \} |
35 + 47 w + 13 w^2 + w^3 = 0 \implies w \in \{ -7, -5, -1 \} |
f(c) = 2 + 2 c + c^2, \quad g(w) = 1 + 3 w \implies f(g(w)) = 5 + 12 w + 9 w^2 |
\log_{5}\left(8 + 3 c\right) = 2 \implies c = \frac{17}{3} |
\frac{36}{14} = \frac{18}{7} |
-8 + y = 0 \implies y = 8 |
-8 + 7 u + u^2 = 0 \implies u \in \{ -8, 1 \} |
5 + w = 0 \implies w = -5 |
f(b) = 3 + 2 b + b^2, \quad g(c) = 4 + 3 c \implies f(g(c)) = 27 + 30 c + 9 c^2 |
\frac{d}{dy}\left(y^4\right) = 4 y^3 |
-6 t + t^2 = 0 \implies t \in \{ 0, 6 \} |
f(b) = 2 + 3 b + b^2, \quad g(z) = 3 + z \implies f(g(z)) = 20 + 9 z + z^2 |
\frac{d}{dy}\left(3 \left(2 + y\right)\right) = 3 |
\lim_{z \to 5} \left(0\right) = 0 |
f(t) = 3 + 5 t + t^2, \quad g(y) = 2 + 3 y \implies f(g(y)) = 17 + 27 y + 9 y^2 |
-36 + 24 = -12 |
9 - 32 = -23 |
-26 + 5 = -21 |
-49 + 31 = -18 |
19 + 35 = 54 |
\int \left(4 c^3\right) dc = c^4 + C |
(5, -3, -2) \times (1, -2, -2) = (2, 8, -7) |
f(z) = 2 + z + z^2, \quad g(a) = 1 + 3 a \implies f(g(a)) = 4 + 9 a + 9 a^2 |
32 + 7 = 39 |
\lim_{y \to 1} \left(-4\right) = -4 |
3 z + z^2 = 0 \implies z \in \{ -3, 0 \} |
f(y) = 5 + y + y^2, \quad g(x) = 2 + x \implies f(g(x)) = 11 + 5 x + x^2 |
8 + w = 0 \implies w = -8 |
-192 + 104 v - 18 v^2 + v^3 = 0 \implies v \in \{ 4, 6, 8 \} |
(-4, 5, 1) \times (-3, -3, -2) = (-7, -11, 27) |
-5 + z = 0 \implies z = 5 |
-5 + b = 0 \implies b = 5 |
5 - 7 = -2 |
f(t) = 3 + 3 t + t^2, \quad g(w) = 2 + 3 w \implies f(g(w)) = 13 + 21 w + 9 w^2 |
4 + t = 0 \implies t = -4 |
\log_{5}\left(8 + 3 b\right) = 2 \implies b = \frac{17}{3} |
28 - 31 u + 2 u^2 + u^3 = 0 \implies u \in \{ -7, 1, 4 \} |
\log_{2}\left(6 + 3 b\right) = 1 \implies b = \frac{-4}{3} |
\lim_{z \to 4} \left(z^2\right) = 16 |
\int \left(\cos{\left(x\right)}\right) dx = \sin{\left(x\right)} + C |
-21 - 4 c + c^2 = 0 \implies c \in \{ -3, 7 \} |
f(x) = 2 + 2 x + x^2, \quad g(z) = 4 + 3 z \implies f(g(z)) = 26 + 30 z + 9 z^2 |
28 \cdot 39 = 1092 |
\lim_{v \to 2} \left(2 v\right) = 4 |
\frac{-49}{36} = \frac{-49}{36} |
\frac{d}{dt}\left(\sin{\left(t\right)}\right) = \cos{\left(t\right)} |
\frac{d}{du}\left(-4 + u\right) = 1 |
\lim_{y \to -3} \left(y^3\right) = -27 |
f(c) = 5 + c + c^2, \quad g(v) = 1 + v \implies f(g(v)) = 7 + 3 v + v^2 |
-25 - 30 = -55 |
f(c) = 5 + 4 c + c^2, \quad g(v) = 3 + 3 v \implies f(g(v)) = 26 + 30 v + 9 v^2 |
(1, -4, 5) \times (-3, -1, 2) = (-3, -17, -13) |
(5, -3, -3) \times (3, -2, -4) = (6, 11, -1) |
-35 - 2 b + b^2 = 0 \implies b \in \{ -5, 7 \} |
18 + 27 v + 10 v^2 + v^3 = 0 \implies v \in \{ -6, -3, -1 \} |
f(c) = 5 + 4 c + c^2, \quad g(t) = 1 + 2 t \implies f(g(t)) = 10 + 12 t + 4 t^2 |
(0, -5, 0) \times (3, -1, -3) = (15, 0, 15) |
f(z) = 3 + 3 z + z^2, \quad g(a) = 1 + a \implies f(g(a)) = 7 + 5 a + a^2 |
\frac{d}{dv}\left(-5\right) = 0 |
f(x) = 4 + 2 x + x^2, \quad g(c) = 2 + 2 c \implies f(g(c)) = 12 + 12 c + 4 c^2 |
\frac{d}{dz}\left(z^4\right) = 4 z^3 |
\log_{3}\left(2 + 3 w\right) = 2 \implies w = \frac{7}{3} |
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