audio audioduration (s) 0.83 21 | transcription stringlengths 3 127 | LaTeX stringlengths 7 142 | Source stringclasses 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 |
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