📐

Equation

Pythagorean Theorem

a2+b2=c2a^2 + b^2 = c^2

Quadratic Formula

x=b±b24ac2a🔨x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}🔨

Einstein's Mass-Energy Equivalence

E=mc2E = mc^2

Integral of a Function

abf(x),dx=F(b)F(a)\int_a^b f(x) , dx = F(b) - F(a)

Differential Equation

dydx=ky\frac{dy}{dx} = ky

Taylor Series Expansion

f(x)=f(a)+f(a)(xa)+f(a)2!(xa)2+f(a)3!(xa)3+f(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + \cdots

Circle Equation

x2+y2=r2x^2 + y^2 = r^2

Logarithmic Identity

loga(b)=logc(b)logc(a)\log_a(b) = \frac{\log_c(b)}{\log_c(a)}

Euler's Formula

eiθ=cos(θ)+isin(θ)e^{i\theta} = \cos(\theta) + i\sin(\theta)

Probability of an Event

P(A)=Number of favorable outcomesTotal number of outcomesP(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
f(x)=n=0f(n)(a)n!(xa)n=f(a)+f(a)(xa)+f(a)2!(xa)2+f(a)3!(xa)3+f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x - a)^n = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + \cdots