∫
−
1
1
f
(
x
)
d
x
=
∑
i
=
1
n
c
i
f
(
x
i
)
{\displaystyle \int _{-1}^{1}f(x)dx=\sum _{i=1}^{n}c_{i}f(x_{i})}
ϕ
=
Δ
t
ω
=
2
π
Δ
t
P
=
2
π
Δ
t
f
{\displaystyle \phi =\Delta t\,\omega =2\pi \,{\frac {\Delta t}{P}}=2\pi \,\Delta t\,f}
λ
2
+
9
=
0
{\displaystyle \lambda ^{2}+9=0}
λ
2
=
−
9
{\displaystyle \lambda ^{2}=-9}
λ
=
−
9
{\displaystyle \lambda ={\sqrt {-9}}}
λ
=
(
−
1
)
(
9
)
=
−
1
9
=
i
3
{\displaystyle \lambda ={\sqrt {(-1)(9)}}={\sqrt {-1}}{\sqrt {9}}=i3}
∑
n
=
1
∞
∫
g
(
n
)
h
(
n
)
f
(
x
)
d
x
{\displaystyle \sum _{n=1}^{\infty }\int _{g(n)}^{h(n)}f(x)dx}
∑
n
=
1
∞
∫
0
1
/
x
(
x
1
/
2
)
/
(
x
2
+
1
)
d
x
{\displaystyle \sum _{n=1}^{\infty }\int _{0}^{1/x}(x^{1/2})/(x^{2}+1)dx}
∫
x
a
4
+
x
2
d
x
=
−
1
2
a
2
l
n
x
+
a
2
x
+
a
2
x
−
a
2
x
+
a
2
+
1
a
2
a
r
c
t
g
a
2
x
a
2
−
x
{\displaystyle \int {\frac {\sqrt {x}}{a^{4}+x^{2}}}dx=-{\frac {1}{2a{\sqrt {2}}}}\,ln{\frac {x+a{\sqrt {2x}}+a^{2}}{x-a{\sqrt {2x}}+a^{2}}}+{\frac {1}{a{\sqrt {2}}}}arctg{\frac {a{\sqrt {2x}}}{a^{2}-x}}}
lim
x
→
∞
10
x
2
+
7
x
+
1
2
x
−
9
=
lim
x
→
∞
20
x
+
7
2
=
∞
{\displaystyle \lim _{x\to \infty }{\frac {10x^{2}+7x+1}{2x-9}}=\lim _{x\to \infty }{\frac {20x+7}{2}}=\infty }
Dividiendo por x al mayor exponente
editar
lim
x
→
∞
10
x
2
+
7
x
+
1
2
x
−
9
=
lim
x
→
∞
10
x
2
x
2
+
7
x
x
2
+
1
x
2
2
x
x
2
−
9
x
2
=
lim
x
→
∞
10
+
7
x
+
1
x
2
2
x
−
9
x
2
=
∞
{\displaystyle \lim _{x\to \infty }{\frac {10x^{2}+7x+1}{2x-9}}=\lim _{x\to \infty }{\frac {{\frac {10x^{2}}{x^{2}}}+{\frac {7x}{x^{2}}}+{\frac {1}{x^{2}}}}{{\frac {2x}{x^{2}}}-{\frac {9}{x^{2}}}}}=\lim _{x\to \infty }{\frac {10+{\frac {7}{x}}+{\frac {1}{x^{2}}}}{{\frac {2}{x}}-{\frac {9}{x^{2}}}}}=\infty }
