ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) ε = -dΦ/dt ∫ u dv = uv - ∫ v du c = λf m = f'(x) p = mv Normality = Molarity × n V = (4/3)πr³ pH = -log[H⁺] ΔG = ΔH - TΔS (1+x)ⁿ = Σ ⁿ C _k.x^k I = ½ Σ c_i z_i² ΔT_f = iK_fm cos 2θ = cos²θ - sin²θ f''(x) P(n, r) = n!/(n-r)! s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) sin 2θ = 2 sinθ cosθ (f(g(x)))' = f'(g(x))⋅g'(x) sin²θ + cos²θ = 1 K.E. = ½mv² Φ = BA cosθ d/dx(ln x) = 1/x 2 sin A cos B = sin(A+B) + sin(A-B) ∫(dx/x) = ln|x| + C

A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| v = u + at (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² S_n = a(1 - rⁿ)/(1 - r) cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! A = ab sinθ E = VIt sin²(θ/2) = (1 - cosθ)/2 F_x + F_y(dy/dx) = 0 C(n, r) = n!/(r!(n-r)!) f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ x = a sinθ M = moles/volume lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) π = MRT U = mgh A = ∫_a^b f(x) dx A = ½ab sin C V = L(dI/dt) sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) T = 2π√(L/g) W = Fd cosθ cos²(θ/2) = (1 + cosθ)/2 m = (y₂ - y₁)/(x₂ - x₁)

d/dx(cos x) = -sin x A = Pe^rt F = q(E + v × B) αβ = c/a α + β = -b/a (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ F = ma n₁ sinθ₁ = n₂ sinθ₂ P = IV F = k( q₁q₂ )/r² K_c = ([C]^c[D]^d)/([A]^a[B]^b) d/dx(sin x) = cos x (x-h)² + (y-k)² = r² E = hf E = E° - (0.0591/n) log Q y - y₁ = m(x - x₁) F_c = mv²/r s = ut + ½at² Q = It P = W/t e = (v₂ - v₁)/(u₁ - u₂) x = [-b ± √(b² - 4ac)]/(2a) d/dx(e^x) = e^x S = a/(1 - r)

f'(a) = lim_h→0 (f(a+h)-f(a))/h λ = h/p Equivalent Weight = Molecular Weight/n Rate = k[A]^m[B]ⁿ d = √((x₂-x₁)²+(y₂-y₁)²) n = mass/M e^x = Σ xⁿ/n! log_b a = ln a/ln b P_solution = X_solvent × P^°_solvent pK_a = -log K_a V = IR S_n = (n/2)[2a + (n - 1)d] n = c/v d = |Ax₀ + By₀ + C|/√(A²+B²) a_c = v²/r Percent Purity = (mass of pure substance/mass of sample) × 100 A = πab a_n = a + (n - 1)d a_n = ar^{n - 1} v² = u² + 2as 1/f = 1/v + 1/u ΔT_b = iK_bm