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f(v) = 2 + 5 v + v^2, \quad g(x) = 2 + 3 x \implies f(g(x)) = 16 + 27 x + 9 x^2 |
\frac{d}{dy}\left(\cos{\left(y\right)}\right) = -\sin{\left(y\right)} |
\lim_{z \to 5} \left(0\right) = 0 |
(-4, 5, 0) \times (1, -4, 0) = (0, 0, 11) |
\frac{d}{db}\left(b\right) = 1 |
\frac{-23}{4} = \frac{-23}{4} |
0 - 45 = -45 |
\int \left(2 t\right) dt = t^2 + C |
\log_{5}\left(3 + 3 t\right) = 1 \implies t = \frac{2}{3} |
\frac{d}{dw}\left(w^2\right) = 2 w |
12 - 7 t + t^2 = 0 \implies t \in \{ 3, 4 \} |
(4, -5, 1) \times (0, -4, -3) = (19, 12, -16) |
\lim_{w \to -3} \left(w^2\right) = 9 |
f(w) = 3 + 5 w + w^2, \quad g(y) = 1 + y \implies f(g(y)) = 9 + 7 y + y^2 |
5 + z = 0 \implies z = -5 |
22 - 39 = -17 |
\int \left(4 c^3\right) dc = c^4 + C |
\int \left(1\right) dt = t + C |
f(y) = 3 + y + y^2, \quad g(c) = 3 + c \implies f(g(c)) = 15 + 7 c + c^2 |
-1 + 3 = 2 |
-3 + c = 0 \implies c = 3 |
-3 z + z^2 = 0 \implies z \in \{ 0, 3 \} |
\int \left(-6\right) dc = -6 c + C |
25 \cdot 29 = 725 |
(-2, 5, -1) \times (-4, 5, 1) = (10, 6, 10) |
\frac{24}{17} = \frac{24}{17} |
8 + t = 0 \implies t = -8 |
(-5, -5, -1) \times (0, -3, -5) = (22, -25, 15) |
-2 + x = 0 \implies x = 2 |
6 + y = 0 \implies y = -6 |
f(v) = 5 + v + v^2, \quad g(z) = 2 + z \implies f(g(z)) = 11 + 5 z + z^2 |
\lim_{b \to 1} \left(5 + b\right) = 6 |
84 - 40 v - 3 v^2 + v^3 = 0 \implies v \in \{ -6, 2, 7 \} |
21 \cdot 19 = 399 |
-8 + 7 t + t^2 = 0 \implies t \in \{ -8, 1 \} |
-46 - 13 = -59 |
13 \cdot 5 = 65 |
\frac{-22}{17} = \frac{-22}{17} |
\int \left(3 b^2 \cos{\left(b\right)} - b^3 \sin{\left(b\right)}\right) db = b^3 \cos{\left(b\right)} + C |
\left(-a + z\right) \cos{\left(a\right)} = -a \cos{\left(a\right)} + z \cos{\left(a\right)} |
\int \left(\cos{\left(x\right)}\right) dx = \sin{\left(x\right)} + C |
\log_{4}\left(5 + 2 z\right) = 2 \implies z = \frac{11}{2} |
4 + t = 0 \implies t = -4 |
5 + v = 0 \implies v = -5 |
\lim_{a \to -1} \left(a\right) = -1 |
\frac{-20}{25} = \frac{-4}{5} |
-10 \cdot 38 = -380 |
42 - 7 = 35 |
(1, 4, 0) \times (-4, 1, -5) = (-20, 5, 17) |
(3, -2, 5) \times (2, 1, -4) = (3, 22, 7) |
\lim_{x \to -3} \left(7 + x\right) = 4 |
f(v) = 2 + 3 v + v^2, \quad g(x) = 4 + 2 x \implies f(g(x)) = 30 + 22 x + 4 x^2 |
\log_{3}\left(7 + 4 w\right) = 3 \implies w = 5 |
\frac{d}{db}\left(2 b^2\right) = 4 b |
2 + c = 0 \implies c = -2 |
3 + b = 0 \implies b = -3 |
\log_{3}\left(7 + 2 y\right) = 3 \implies y = 10 |
\log_{2}\left(7 + b\right) = 3 \implies b = 1 |
2 + w = 0 \implies w = -2 |
(4, -4, 4) \times (-4, -4, 2) = (8, -24, -32) |
-8 - 27 = -35 |
(1, -2, -1) \times (2, 2, 1) = (0, -3, 6) |
-4 + y = 0 \implies y = 4 |
(1, -1, -1) \times (-2, -2, -4) = (2, 6, -4) |
\log_{4}\left(5 + 4 w\right) = 1 \implies w = \frac{-1}{4} |
\frac{d}{dx}\left(\sin{\left(x\right)} \left(-2 + x\right)\right) = \cos{\left(x\right)} \left(-2 + x\right) + \sin{\left(x\right)} |
\frac{-50}{49} = \frac{-50}{49} |
(3, -1, -5) \times (-3, 3, 4) = (11, 3, 6) |
f(x) = 1 + 2 x + x^2, \quad g(z) = 2 + z \implies f(g(z)) = 9 + 6 z + z^2 |
-7 + c = 0 \implies c = 7 |
-7 + z = 0 \implies z = 7 |
\log_{3}\left(4 + 3 v\right) = 1 \implies v = \frac{-1}{3} |
f(v) = 3 + v + v^2, \quad g(z) = 3 + z \implies f(g(z)) = 15 + 7 z + z^2 |
24 - 4 x - 6 x^2 + x^3 = 0 \implies x \in \{ -2, 2, 6 \} |
f(w) = 2 + 4 w + w^2, \quad g(x) = 1 + 2 x \implies f(g(x)) = 7 + 12 x + 4 x^2 |
-28 \cdot 7 = -196 |
\log_{4}\left(6 + 2 b\right) = 1 \implies b = -1 |
-37 + 38 = 1 |
-3 + 48 = 45 |
48 + 34 w - 13 w^2 + w^3 = 0 \implies w \in \{ -1, 6, 8 \} |
(0, -4, 1) \times (3, -4, -1) = (8, 3, 12) |
\log_{2}\left(5 + 4 v\right) = 2 \implies v = \frac{-1}{4} |
44 \cdot 35 = 1540 |
-4 b + b^2 = 0 \implies b \in \{ 0, 4 \} |
2 - 3 c + c^2 = 0 \implies c \in \{ 1, 2 \} |
\frac{d}{db}\left(b\right) = 1 |
(-4, -2, -1) \times (4, 5, -4) = (13, -20, -12) |
-56 - 22 x + 5 x^2 + x^3 = 0 \implies x \in \{ -7, -2, 4 \} |
\lim_{a \to -1} \left(-10 + a\right) = -11 |
42 - 13 w + w^2 = 0 \implies w \in \{ 6, 7 \} |
\int \left(\cos{\left(x\right)}\right) dx = \sin{\left(x\right)} + C |
\lim_{c \to -4} \left(2 + c\right) = -2 |
\lim_{c \to 1} \left(c\right) = 1 |
\log_{2}\left(6 + 2 v\right) = 3 \implies v = 1 |
-9 + x^2 = 0 \implies x \in \{ -3, 3 \} |
0 - 17 = -17 |
(-3, -1, 3) \times (-5, 4, 3) = (-15, -6, -17) |
-24 z + 5 z^2 + z^3 = 0 \implies z \in \{ -8, 0, 3 \} |
\frac{d}{da}\left(2 a\right) = 2 |
-21 + 4 y + y^2 = 0 \implies y \in \{ -7, 3 \} |
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