(Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ V = IR T = 2π√(L/g) Equivalent Weight = Molecular Weight/n ΔT_f = iK_fm sin 2θ = 2 sinθ cosθ (1+x)ⁿ = Σ ⁿ C _k.x^k α + β = -b/a n = mass/M A = ab sinθ f'(a) = lim_h→0 (f(a+h)-f(a))/h n = c/v a_c = v²/r s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) A = ½ab sin C F = k( q₁q₂ )/r² Φ = BA cosθ d = √((x₂-x₁)²+(y₂-y₁)²) 2 sin A cos B = sin(A+B) + sin(A-B) (x-h)² + (y-k)² = r² v² = u² + 2as v = u + at p = mv e^x = Σ xⁿ/n!

e = (v₂ - v₁)/(u₁ - u₂) Rate = k[A]^m[B]ⁿ P(n, r) = n!/(n-r)! f''(x) C(n, r) = n!/(r!(n-r)!) x = a sinθ E = VIt K_c = ([C]^c[D]^d)/([A]^a[B]^b) sin²θ + cos²θ = 1 (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k d/dx(e^x) = e^x A = ∫_a^b f(x) dx V = L(dI/dt) pK_a = -log K_a λ = h/p K.E. = ½mv² U = mgh Q = It P_solution = X_solvent × P^°_solvent ∫ u dv = uv - ∫ v du y - y₁ = m(x - x₁) x = [-b ± √(b² - 4ac)]/(2a) a_n = a + (n - 1)d log_b a = ln a/ln b A = πab

(f(g(x)))' = f'(g(x))⋅g'(x) V = (4/3)πr³ A = Pe^rt S = a/(1 - r) sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) n₁ sinθ₁ = n₂ sinθ₂ 1/f = 1/v + 1/u d/dx(cos x) = -sin x a_n = ar^{n - 1} P = W/t Normality = Molarity × n ε = -dΦ/dt F = q(E + v × B) I = ½ Σ c_i z_i² ΔG = ΔH - TΔS d/dx(sin x) = cos x cos²(θ/2) = (1 + cosθ)/2 αβ = c/a W = Fd cosθ d = |Ax₀ + By₀ + C|/√(A²+B²) m = f'(x) F = ma cos 2θ = cos²θ - sin²θ F_c = mv²/r

m = (y₂ - y₁)/(x₂ - x₁) cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! F_x + F_y(dy/dx) = 0 E = hf ∫(dx/x) = ln|x| + C s = ut + ½at² ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) S_n = (n/2)[2a + (n - 1)d] A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| sin²(θ/2) = (1 - cosθ)/2 M = moles/volume c = λf P = IV S_n = a(1 - rⁿ)/(1 - r) π = MRT f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! ΔT_b = iK_bm pH = -log[H⁺] E = E° - (0.0591/n) log Q Percent Purity = (mass of pure substance/mass of sample) × 100 d/dx(ln x) = 1/x