Download Maths for Economics Cheat Sheet and more Cheat Sheet Econometrics and Mathematical Economics in PDF only on Docsity! Maths for Economics PRINCIPLES AND FORMULAE Exponential functions e ≈ 2.7183 is the exponential constant Graph of y = ex showing exponential growth Graph of y = e –x showing exponential decay Quadratic functions y = ax2 + bx + c Total cost functions TC = a + bq – cq2 + dq3 Inverse functions y = a/x = ax–1 q = a/p = ap–1 (1) b2 – 4ac < 0; (2) b2 – 4ac = 0; (3) b2 – 4ac > 0 Differentiation Graphs of Common Functions Integration The sum–difference rule Constant multiples The product rule The quotient rule The chain rule x v x uxvxux d d d d))()((d d ±=± x fkxfkx d d))((d d = x uvx vuuvx d d d d)(d d += 2 d d d d d d v x vux uv v u x – = x u u y x yxuuuyy d d d d d dthen,)(where,)(If .=== x v x uxvxx d d d d))()((d d ±=± x fkxfkx d d))((d d = x uvx vuuvx d d d d)(d d += 2 d d d d d d v x vux uv v u x – = x u u y x yxuuuyy d d d d d dthen,)(where,)(If .=== x v x uxvxux d d d d))()((d d ±=± x fkxfkx d d))((d d = x uvx vuuvx d d d d)(d d += 2 d d d d d d v x vux uv v u x – = x u u y x yxuuuyy d d d d d dthen,)(where,)(If .=== x v x uxvxux d d d d))()((d d ±=± x fkxfkx d d))((d d = x uvx vuuvx d d d d)(d d += 2 d d d d d d v x vux uv v u x – = x u u y x yxuuuyy d d d d d d then ,)( where,)( If .=== ∫ xxf d)(x x f )( cx + c+ 2 2 cx +3 3 x2 e x e kx x , (n = –1)n cx x +n+1 n+1 ck kk, (any) constant c ekx + c+ex ln x + cx = 1/x–1 x v x uxvxux d d d d))()((d d ±=± x fkxfkx d d))((d d = x uvx vuuvx d d d d)(d d += 2 d d d d d d v x vux uv v u x – = x u u y x yxuuuyy d d d d d dthen,)(where,)(If .=== Posi tive grad ient (x1, y1) (x2, y2) 12 12 xx yym – –= Negative gradient (x1, y1) (x2, y2) 12 12 xx yym – –= Posi tive grad ient (x1, y1) (x2, y2) 12 12 xx yym – –= Negative gradient (x1, y1) (x2, y2) 12 12 xx yym – –= Linear y = mx + c; m = gradient; c = vertical intercepty = f (x) k, constant 0 x 1 x2 2x x3 3x2 xn, any constant n nxn–1 ex ex = y ekx kekx = ky e f (x) f’(x)e f(x) ln x 1/x ln kx = loge kx 1/x ln f (x) f’(x)/f(x) dy dx = f’(x) for k constant Studying Economics Fact card 2 5/3/10 16:34 Page 1
