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\lim_{x \to 0} \left(x^4\right) = 0 |
6 + x = 0 \implies x = -6 |
\left(-c + z\right) c z = c z^2 - c^2 z |
-28 - 3 z + z^2 = 0 \implies z \in \{ -4, 7 \} |
-42 \cdot 37 = -1554 |
40 - 13 c + c^2 = 0 \implies c \in \{ 5, 8 \} |
\frac{1}{4} = \frac{1}{4} |
\log_{4}\left(5 + 4 b\right) = 3 \implies b = \frac{59}{4} |
-7 - 47 = -54 |
\log_{3}\left(8 + 2 x\right) = 1 \implies x = \frac{-5}{2} |
-56 - 57 v + v^3 = 0 \implies v \in \{ -7, -1, 8 \} |
8 + c = 0 \implies c = -8 |
\int \left(-\sin{\left(v\right)}\right) dv = -1 + \cos{\left(v\right)} + C |
\log_{2}\left(5 + 4 z\right) = 2 \implies z = \frac{-1}{4} |
-28 + 3 z + z^2 = 0 \implies z \in \{ -7, 4 \} |
f(z) = 5 + 2 z + z^2, \quad g(y) = 3 + y \implies f(g(y)) = 20 + 8 y + y^2 |
-16 \cdot 19 = -304 |
\log_{3}\left(4 + 4 u\right) = 1 \implies u = \frac{-1}{4} |
f(t) = 4 + 2 t + t^2, \quad g(u) = 1 + u \implies f(g(u)) = 7 + 4 u + u^2 |
f(u) = 5 + 2 u + u^2, \quad g(t) = 3 + 3 t \implies f(g(t)) = 20 + 24 t + 9 t^2 |
f(b) = 2 + 5 b + b^2, \quad g(c) = 1 + 2 c \implies f(g(c)) = 8 + 14 c + 4 c^2 |
6 + c = 0 \implies c = -6 |
\lim_{b \to -4} \left(b^2\right) = 16 |
-392 - 49 t + 8 t^2 + t^3 = 0 \implies t \in \{ -8, -7, 7 \} |
u^3 \left(-4 + u\right) = -4 u^3 + u^4 |
-48 - 28 = -76 |
-13 + 33 = 20 |
28 - 6 = 22 |
f(x) = 1 + x + x^2, \quad g(z) = 1 + z \implies f(g(z)) = 3 + 3 z + z^2 |
\log_{4}\left(2 + 4 z\right) = 2 \implies z = \frac{7}{2} |
f(v) = 1 + 3 v + v^2, \quad g(u) = 2 + u \implies f(g(u)) = 11 + 7 u + u^2 |
\frac{21}{23} = \frac{21}{23} |
-20 + t + t^2 = 0 \implies t \in \{ -5, 4 \} |
\frac{d}{dz}\left(7 z\right) = 7 |
(3, 5, -1) \times (0, -4, 4) = (16, -12, -12) |
\lim_{w \to -5} \left(w^2\right) = 25 |
\frac{23}{7} = \frac{23}{7} |
-96 - 52 x + x^3 = 0 \implies x \in \{ -6, -2, 8 \} |
-2 - 2 = -4 |
\log_{4}\left(6 + a\right) = 2 \implies a = 10 |
\log_{4}\left(2 + 4 c\right) = 1 \implies c = \frac{1}{2} |
\log_{5}\left(6 + 4 b\right) = 2 \implies b = \frac{19}{4} |
f(x) = 4 + 4 x + x^2, \quad g(y) = 3 + 2 y \implies f(g(y)) = 25 + 20 y + 4 y^2 |
2 - 3 z + z^2 = 0 \implies z \in \{ 1, 2 \} |
\int \left(1\right) dy = y + C |
\lim_{t \to -1} \left(0\right) = 0 |
f(v) = 1 + 3 v + v^2, \quad g(a) = 2 + 3 a \implies f(g(a)) = 11 + 21 a + 9 a^2 |
\int \left(6 y^2\right) dy = 2 y^3 + C |
(0, -4, -5) \times (4, -4, 5) = (-40, -20, 16) |
\lim_{a \to 4} \left(7 a\right) = 28 |
z^3 \left(3 - b\right) = -b z^3 + 3 z^3 |
\lim_{c \to -3} \left(\sin{\left(c\right)}\right) = -\sin{\left(3\right)} |
30 - 32 = -2 |
c \left(4 - c\right) = 4 c - c^2 |
\lim_{x \to 4} \left(x\right) = 4 |
\lim_{y \to 4} \left(\sin{\left(y\right)}\right) = \sin{\left(4\right)} |
-56 a - a^2 + a^3 = 0 \implies a \in \{ -7, 0, 8 \} |
\log_{4}\left(2 + 4 x\right) = 2 \implies x = \frac{7}{2} |
-3 \cdot 3 = -9 |
\lim_{x \to 2} \left(x\right) = 2 |
\frac{48}{15} = \frac{16}{5} |
-18 - 26 = -44 |
18 \left(-t + z\right) = -18 t + 18 z |
-28 + 3 t + t^2 = 0 \implies t \in \{ -7, 4 \} |
4 + u = 0 \implies u = -4 |
f(u) = 4 + 4 u + u^2, \quad g(t) = 2 + 2 t \implies f(g(t)) = 16 + 16 t + 4 t^2 |
-6 b + b^2 = 0 \implies b \in \{ 0, 6 \} |
\int \left(-\sin{\left(z\right)}\right) dz = -1 + \cos{\left(z\right)} + C |
\log_{5}\left(5 + 2 c\right) = 3 \implies c = 60 |
\frac{d}{db}\left(1\right) = 0 |
\lim_{b \to -2} \left(2 b\right) = -4 |
z = 0 \implies z = 0 |
\frac{d}{db}\left(4 - b + b^4\right) = -1 + 4 b^3 |
\int \left(1\right) dy = y + C |
f(v) = 3 + v + v^2, \quad g(w) = 3 + 3 w \implies f(g(w)) = 15 + 21 w + 9 w^2 |
\log_{3}\left(4 + 3 b\right) = 1 \implies b = \frac{-1}{3} |
\frac{16}{22} = \frac{8}{11} |
\frac{-8}{22} = \frac{-4}{11} |
(5, -5, 5) \times (0, 2, 2) = (-20, -10, 10) |
f(a) = 2 + 3 a + a^2, \quad g(z) = 2 + z \implies f(g(z)) = 12 + 7 z + z^2 |
\int \left(-8\right) da = -8 a + C |
24 - 14 = 10 |
\lim_{u \to 1} \left(u^2\right) = 1 |
\lim_{t \to 4} \left(0\right) = 0 |
4 - 5 w + w^2 = 0 \implies w \in \{ 1, 4 \} |
7 + z = 0 \implies z = -7 |
6 \cdot 43 = 258 |
\log_{2}\left(2 + 4 z\right) = 2 \implies z = \frac{1}{2} |
\log_{3}\left(6 + 4 c\right) = 1 \implies c = \frac{-3}{4} |
f(u) = 1 + 2 u + u^2, \quad g(b) = 4 + 2 b \implies f(g(b)) = 25 + 20 b + 4 b^2 |
f(v) = 2 + 5 v + v^2, \quad g(c) = 3 + 2 c \implies f(g(c)) = 26 + 22 c + 4 c^2 |
\lim_{u \to -2} \left(u^2\right) = 4 |
(-5, -3, 0) \times (1, 3, 0) = (0, 0, -12) |
-5 + u = 0 \implies u = 5 |
(-1, 2, -5) \times (-4, 1, -3) = (-1, 17, 7) |
\frac{d}{dc}\left(c^2\right) = 2 c |
f(c) = 1 + 2 c + c^2, \quad g(u) = 4 + u \implies f(g(u)) = 25 + 10 u + u^2 |
39 - 24 = 15 |
f(a) = 4 + 5 a + a^2, \quad g(y) = 3 + y \implies f(g(y)) = 28 + 11 y + y^2 |
-14 u - 5 u^2 + u^3 = 0 \implies u \in \{ -2, 0, 7 \} |
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