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audioduration (s)
0.83
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transcription
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89 values
1 over n to the 5th square root
$(1/\sqrt{n^{5}})$
https://www.youtube.com/watch?v=MK_0QHbUnIA
n plus 1 times c n plus 1 divided by n plus 1
$(n+1)c_{n+1}/(n+1)$
https://www.youtube.com/watch?v=wOHrNt9ScYs
1 over 1 minus x
$\frac{1}{1-x}$
https://www.youtube.com/watch?v=wOHrNt9ScYs
s times one minus x
$s\cdot(1-x)$
https://www.youtube.com/watch?v=wOHrNt9ScYs
minus r less than x less than r
$-r<x<r$
https://www.youtube.com/watch?v=wOHrNt9ScYs
sum a n x to the n
$\sum {a_n}x^{n}$
https://www.youtube.com/watch?v=wOHrNt9ScYs
a1 x squared over 2
$\frac{\mathbb{a_1} x^{2}}{2}$
https://www.youtube.com/watch?v=wOHrNt9ScYs
a zero plus a one x plus a two x squared plus a three x cubed plus dot dot dot
$\displaystyle \mathcal{a}_{0}+\mathcal{a}_{1}x+\mathcal{a}_{2}x^{2}+\mathcal{a}_{3}x^{3}+\cdots$
https://www.youtube.com/watch?v=wOHrNt9ScYs
a n is equal to f nth derivative divided by n factorial
$a_n\mathrel{\mathop{}}=\frac{f^{n}}{n!}$
https://www.youtube.com/watch?v=wOHrNt9ScYs
the sum n equals 0 to infinity of 1 divided by n factorial x to the n
$\sum_{n=0}^{\infty}\frac{1}{n!}x^{n}$
https://www.youtube.com/watch?v=wOHrNt9ScYs
x minus x cubed over 3 factorial plus x to the 5th over 5 factorial
$x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}$
https://www.youtube.com/watch?v=wOHrNt9ScYs
x to the seventh over seven factorial
$x^{7}/7!$
https://www.youtube.com/watch?v=wOHrNt9ScYs
x to the fourth over four factorial
$x^{4}/4!$
https://www.youtube.com/watch?v=wOHrNt9ScYs
1 over 2 factorial times x squared plus 1 over 3 factorial times x cubed
$\displaystyle{1\over2!}x^{2}+{1\over3!}x^{3}$
https://www.youtube.com/watch?v=--lPz7VFnKI
1 over 1 plus x
$\frac{1}{1+x}$
https://www.youtube.com/watch?v=--lPz7VFnKI
x over 2n plus 1
$\frac{x}{2n+1}$
https://www.youtube.com/watch?v=--lPz7VFnKI
x times the sine of x
$x\mathinner{\sin\left(x\right)}$
https://www.youtube.com/watch?v=--lPz7VFnKI
x squared minus x to the fourth over three factorial plus x to the sixth over five factorial
$x^{2}-\frac{x^{4}}{3!}+\frac{x^{6}}{5!}$
https://www.youtube.com/watch?v=--lPz7VFnKI
the integral from zero to x of dt over one plus x
$\int_{0}^{x}\frac{dt}{1+x}$
https://www.youtube.com/watch?v=--lPz7VFnKI
1 minus t plus t squared minus t cubed
$1-t+t^{2}-t^{3}$
https://www.youtube.com/watch?v=--lPz7VFnKI
x minus x squared over two plus x cubed over three minus x to the fourth over four
$x-x^{2}/2+x^{3}/3-x^{4}/4$
https://www.youtube.com/watch?v=--lPz7VFnKI
x equals minus t squared
$x=-t^{2}$
https://www.youtube.com/watch?v=--lPz7VFnKI
t to the fourth over two factorial
$\frac{t^{4}}{2!}$
https://www.youtube.com/watch?v=--lPz7VFnKI
two over the square root of pi
$2/\sqrt{\pi}$
https://www.youtube.com/watch?v=--lPz7VFnKI
integral of e to the minus t squared dt from 0 to x
$\int_{0}^{x}(e^{-t^{2}})dt$
https://www.youtube.com/watch?v=--lPz7VFnKI
x minus x cubed over 3
$x-\frac{x^{3}}{3}$
https://www.youtube.com/watch?v=--lPz7VFnKI
5 times 2 factorial
$5\cdot2!$
https://www.youtube.com/watch?v=--lPz7VFnKI
minus x to the seventh over seven times three factorial
$-\frac{x^{7}}{7\cdot3!}$
https://www.youtube.com/watch?v=--lPz7VFnKI
z of t minus two equals minus three t
$z(t-2)=-3t$
https://www.youtube.com/watch?v=57jzPlxf4fk
minus one plus two t
$\displaystyle -1+2t$
https://www.youtube.com/watch?v=57jzPlxf4fk
x plus two y plus four z equals seven
$x+2y+4z=7$
https://www.youtube.com/watch?v=57jzPlxf4fk
x of t plus twice y of t plus four z of t
$x(t)+2y(t)+4z(t)$
https://www.youtube.com/watch?v=57jzPlxf4fk
minus one plus two t plus twice two plus t plus four times two minus three t
$-1+2t+2(2+t)+4(2-3t)$
https://www.youtube.com/watch?v=57jzPlxf4fk
minus 8t plus 11 equals 7
$-8t+11=7$
https://www.youtube.com/watch?v=57jzPlxf4fk
minus one plus two t will be zero
$-1+2t=0\operatorname{}$
https://www.youtube.com/watch?v=57jzPlxf4fk
a minus a cosine theta
$a-a\cos\theta$
https://www.youtube.com/watch?v=57jzPlxf4fk
x of theta is theta minus sine theta
$x(\theta)=\theta-\sin\theta$
https://www.youtube.com/watch?v=57jzPlxf4fk
t squared over two
$\frac{t^{2}}{2}$
https://www.youtube.com/watch?v=57jzPlxf4fk
theta minus theta cubed over six
$\theta-\frac{\theta-\theta^{3}}{6}$
https://www.youtube.com/watch?v=57jzPlxf4fk
t minus sine t
$t-\sin t$
https://www.youtube.com/watch?v=0D4BbCa4gHo
square root of one minus cosine t squared plus sine squared t
$\sqrt{1-\cos^{2}t+\sin^{2}t}$
https://www.youtube.com/watch?v=0D4BbCa4gHo
square root of one minus two cosine t plus cosine squared t plus sine squared t
$\displaystyle \sqrt{1-2\cos t+\cos^{2}t+\sin^{2}t}$
https://www.youtube.com/watch?v=0D4BbCa4gHo
square root of two minus two cosine t
$\sqrt{2-2\cos t}$
https://www.youtube.com/watch?v=0D4BbCa4gHo
F equals ma
$\mathcal{F}=\mathcal{ma}$
https://www.youtube.com/watch?v=0D4BbCa4gHo
v divided by magnitude of v
$v/||v||$
https://www.youtube.com/watch?v=0D4BbCa4gHo
uv prime equals u prime v plus u v prime
$(uv)^{\prime}=u^{\prime}v+uv^{\prime}$
https://www.youtube.com/watch?v=0D4BbCa4gHo
dr dt cross v plus r cross dv dt
$\displaystyle\frac{d\mathbf{r}}{dt}\times\mathbf{v}+\mathbf{r}\times\frac{d\mathbf{v}}{dt}$
https://www.youtube.com/watch?v=0D4BbCa4gHo
determinant of A is not zero
$\det(A)\neq0$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
x plus 3y plus z equals zero
$x+3y+z=0.$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
x plus y equals zero
$x+y=0$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
minus 2x minus z will be x plus 3y plus z
$-2x-z\operatorname{=}x+3y+z$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
x plus y plus two z
$\displaystyle x+y+2z$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
dr dt dot r plus r dot dr dt
$\frac{dr}{dt}\cdot r+r\cdot\frac{dr}{dt}$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
r dot v is zero
$\displaystyle \mathbf{r}\cdot\mathbf{v}=0$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
r is perpendicular to v
$\displaystyle \textbf{r}\operatorname{\perp} \mathcal{v}$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
dr dt is v dot v plus r dot dv dt is going to be zero
$ \frac{dr}{dt}=v{{\cdot}}v+r\cdot\frac{dv}{dt}=0$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
f of x y equals one over x plus y
$f(x,y)=\frac{1}{x+y}$
https://www.youtube.com/watch?v=dK3NEf13nPc
z equals f of x y
${z}=f(x,y)$
https://www.youtube.com/watch?v=dK3NEf13nPc
f of x, y equals one minus x squared minus y squared
$f(x,y)=1-x^{2}-y^{2}$
https://www.youtube.com/watch?v=dK3NEf13nPc
z equals one minus x squared minus y squared
$z=1-x^{2}-y^{2}$
https://www.youtube.com/watch?v=dK3NEf13nPc
f of x y equals minus y
$f(x,y)=-y$
https://www.youtube.com/watch?v=dK3NEf13nPc
x squared plus y squared equals zero
$x^{2}+y^{2}=0$
https://www.youtube.com/watch?v=dK3NEf13nPc
f prime at x0 times delta x
$f^{\prime}(x_{0})\times\Delta x$
https://www.youtube.com/watch?v=dK3NEf13nPc
x0 plus h
$\mathcal{x}_{0}+h$
https://www.youtube.com/watch?v=dK3NEf13nPc
z0 plus a times x minus x0 plus b times y minus y0
$z_0+a(x-x_0)+b(y-y_0)$
https://www.youtube.com/watch?v=UYe98CcxPbs
x squared minus 2xy
$x^{2}-2xy$
https://www.youtube.com/watch?v=UYe98CcxPbs
x minus y squared
$(x -y^{2})$
https://www.youtube.com/watch?v=UYe98CcxPbs
2x minus 2y
$\displaystyle 2x-2y$
https://www.youtube.com/watch?v=UYe98CcxPbs
twice x minus y
$2\mathrm{(x - y)}$
https://www.youtube.com/watch?v=UYe98CcxPbs
x minus y plus one squared
$(x-y+1)^{2}$
https://www.youtube.com/watch?v=UYe98CcxPbs
axi plus b
$\mathtt{ax_i+b}$
https://www.youtube.com/watch?v=UYe98CcxPbs
yi minus axi
$y_{i}-ax_{i}$
https://www.youtube.com/watch?v=UYe98CcxPbs
xi squared times a plus xi times b
$x_i^2\times a+x_i\times b$
https://www.youtube.com/watch?v=UYe98CcxPbs
sum of xi yi
$\mathsf{\sum_{i}(x_{i} y_{i})}$
https://www.youtube.com/watch?v=UYe98CcxPbs
y equals a constant times exponential of a times x
$y=\text{c}\exp(ax)$
https://www.youtube.com/watch?v=UYe98CcxPbs
a x squared plus b x plus c
$ax^{2}+bx+c$
https://www.youtube.com/watch?v=UYe98CcxPbs
a x squared plus b xy plus c y squared
$ay^{2}+bxy+cy^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
x squared plus 2xy
$x^{2}+2xy$
https://www.youtube.com/watch?v=3_goGnJm5sA
a times x squared plus b over a xy
$a(x^{2}+\frac{b}{a}xy)$
https://www.youtube.com/watch?v=3_goGnJm5sA
b squared over 4a y squared
$\frac{b^2}{4a}y^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
a times x squared plus a times 2xb over 2ay
$ax^{2}+a\frac{2xb}{2ay}$
https://www.youtube.com/watch?v=3_goGnJm5sA
b squared over 4 a squared y squared plus cy squared minus b squared over 4 a y squared
$\displaystyle \frac{b^{2}}{4a^{2}}y^{2}+cy^{2}-\frac{b^{2}}{4a}y^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
one over four a
$\frac{1}{4a}$
https://www.youtube.com/watch?v=3_goGnJm5sA
four ac minus b squared y squared
$4ac-b^{2}y^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
u equals x plus b over two ay
$u =x+\frac{b}{2a}y$
https://www.youtube.com/watch?v=3_goGnJm5sA
four a c minus b squared equals zero
$4ac-b^{2}=0$
https://www.youtube.com/watch?v=3_goGnJm5sA
f of x equals x to the five
$f(x)=x^{5}$
https://www.youtube.com/watch?v=3_goGnJm5sA
a times x plus b over 2a times y squared
$\displaystyle a(x+\frac{b}{2a}y)^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
y squared times a times x over y squared
$y^{2}a(x/y)^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
a t squared plus b t plus c
$at^{2}+bt+c$
https://www.youtube.com/watch?v=3_goGnJm5sA
ax over y squared plus bx over y plus c
$a(x/y)^{2}+b(x/y)+c$
https://www.youtube.com/watch?v=3_goGnJm5sA
w sub y is bx plus 2cy
$w_y=bx+{2}cy$
https://www.youtube.com/watch?v=3_goGnJm5sA
x minus x zero squared
$(x-x_{0})^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
f sub xy times change in x times change in y plus one half of fyy times y minus y0 squared
$\displaystyle f_{xy}\cdot\Delta x\cdot\Delta y+\frac{1}{2}f_{yy}(y-y_{0})^{2}$
https://www.youtube.com/watch?v=3_goGnJm5sA
f of x y equals x plus y plus 1 over xy
$f(x,y)=x+y+\frac{1}{xy}$
https://www.youtube.com/watch?v=3_goGnJm5sA
two over x cubed y
$\operatorname{\frac{2}{(x^{3}y)}}$
https://www.youtube.com/watch?v=3_goGnJm5sA
two over xy cubed
$\frac{2}{xy^{3}}$
https://www.youtube.com/watch?v=3_goGnJm5sA
dy equals f prime of x times dx
$dy=f^{\prime}(x)dx$
https://www.youtube.com/watch?v=7eZVshlT33Q
dy over dx is going to be one over cosine y
$\mathrm{\frac{\mathrm{d}y}{dx}}\rightarrow\frac{1}{\cos y}$
https://www.youtube.com/watch?v=7eZVshlT33Q
one over square root of one minus x squared
$\frac{1}{\sqrt{(1-x^{2})}}$
https://www.youtube.com/watch?v=7eZVshlT33Q