a_c = v²/r A = ∫_a^b f(x) dx ΔT_b = iK_bm W = Fd cosθ T = 2π√(L/g) ∫(dx/x) = ln|x| + C Equivalent Weight = Molecular Weight/n f'(a) = lim_h→0 (f(a+h)-f(a))/h cos²(θ/2) = (1 + cosθ)/2 ΔG = ΔH - TΔS S_n = a(1 - rⁿ)/(1 - r) n = c/v a_n = ar^{n - 1} m = f'(x) E = VIt P = IV E = E° - (0.0591/n) log Q (x-h)² + (y-k)² = r² ε = -dΦ/dt pK_a = -log K_a sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) P = W/t d/dx(sin x) = cos x C(n, r) = n!/(r!(n-r)!)

A = Pe^rt F_x + F_y(dy/dx) = 0 d/dx(ln x) = 1/x pH = -log[H⁺] a_n = a + (n - 1)d A = ½ab sin C s = ut + ½at² A = πab F = k( q₁q₂ )/r² cos 2θ = cos²θ - sin²θ Percent Purity = (mass of pure substance/mass of sample) × 100 M = moles/volume S_n = (n/2)[2a + (n - 1)d] V = IR d/dx(cos x) = -sin x K.E. = ½mv² Φ = BA cosθ K_c = ([C]^c[D]^d)/([A]^a[B]^b) v² = u² + 2as s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) v = u + at P(n, r) = n!/(n-r)! log_b a = ln a/ln b d/dx(e^x) = e^x f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ

α + β = -b/a lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ x = [-b ± √(b² - 4ac)]/(2a) c = λf V = (4/3)πr³ n₁ sinθ₁ = n₂ sinθ₂ (f(g(x)))' = f'(g(x))⋅g'(x) d = |Ax₀ + By₀ + C|/√(A²+B²) (1+x)ⁿ = Σ ⁿ C _k.x^k λ = h/p Normality = Molarity × n αβ = c/a F = q(E + v × B) A = ab sinθ S = a/(1 - r) F = ma f''(x) F_c = mv²/r p = mv e^x = Σ xⁿ/n! m = (y₂ - y₁)/(x₂ - x₁) P_solution = X_solvent × P^°_solvent

x = a sinθ sin 2θ = 2 sinθ cosθ V = L(dI/dt) ∫ u dv = uv - ∫ v du ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) d = √((x₂-x₁)²+(y₂-y₁)²) E = hf 2 sin A cos B = sin(A+B) + sin(A-B) y - y₁ = m(x - x₁) Q = It sin²θ + cos²θ = 1 I = ½ Σ c_i z_i² A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k ΔT_f = iK_fm e = (v₂ - v₁)/(u₁ - u₂) sin²(θ/2) = (1 - cosθ)/2 Rate = k[A]^m[B]ⁿ π = MRT U = mgh 1/f = 1/v + 1/u n = mass/M