User:NutShell of a Peanut

$$T=2\pi \sqrt{\frac{L}{g}}$$

$$f(x)=x^2$$ $$f'(x)=2x$$ $$\int \,2x\,dx=x^2 = \int \,f'(x)\,dx=f(x)$$

$$\sum_{k=0}^n \binom{n}{k}a^{n-k} b^k$$ $$\binom{n}{k}= \frac{n!}{k!(n-k)!}$$ $$(a+b)^n$$

$$x^2+y^2=r^2$$

$$\frac{x^2}{r^2}+\frac{y^2}{r^2}=1$$ Circle

$$\frac{x^2}{a_s}+\frac{y^2}{b_l}=1$$

$$\int_{x_1}^{x_2} \, \frac{x^2}{r^2}+\frac{y^2}{r^2} \, dx$$  Area of circle

$$\oint_{x_1}^{x_2} \, \frac{x^2}{r^2}+\frac{y^2}{r^2} \, dx \, $$ Circumference of circle

$$G_{\mu\nu}+{\Lambda g}_{\mu\nu}=\frac{8\pi G}{c^4} T_{\mu\nu}$$

$$F_g=G\frac{m_1 m_2}{r^2}$$

Story of the 3 forts

$$\frac{3}{4} \, t_p - t_e=t_{past} \, \frac{F^3}{R^h}$$

$$\oint_4^3 \, P=LW $$ $$\times$$ $$ \aleph_0^{army}>\infty$$

$$\psi\longrightarrow \forall \in C | \exists$$

The End

$$\frac{d}{dx} [\frac{x^{n+1}}{n+1} + C]=x^n $$ $$ \int x^n \, dx =\frac{x^{n+1}}{n+1} + C $$

$$ \sum_{i=1}^n (x_{i-1})\Delta{x}$$

$$\int_b^a \, f(x) \, dx = \sum_{R=1}^R A_R$$

$$\frac{d}{dx} e^x = e^x$$ $$\int e^x \, dx = e^x$$

$$E_k=\frac{1}{2} mv^2$$ $$p=mv$$

$$\frac{p}{m}=v$$

$$ E=\frac{1}{2} m (\frac{p}{m})(\frac{p}{m})$$

$$E=\frac{1}{2}m (\frac{p^2}{m^2}) $$

$$E=\frac{p^2}{2m}$$

$$\frac{d}{dx}\pi {r^2} = 2 \pi {r} $$

$$\int 2 \pi {r} \, dx = \pi {r^2}$$

Sphere

$$\frac {d}{dx} \frac{4}{3} \pi {r^3} = 4\pi{r^2}$$

$$\int 4\pi{r^2} dx = \frac{4}{3}\pi{r^3}$$ $$\int \frac{d}{dx} f(x) dx = f(x)$$

$$f(x,y)=x^2 sin(y)$$

$$\frac{\partial f}{\partial x}=2sin(y)x$$

$$\frac{\partial f}{\partial y}=x^2 cos(y)$$

$$\nabla f = \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}$$