By Knut Sydsæter, Peter Hammond, Arne Strøm

This article presents a useful advent to the mathematical instruments that undergraduate economists want. The insurance is entire, starting from simple algebra to extra complicated fabric, while concentrating on all of the middle issues which are frequently taught in undergraduate classes on arithmetic for economists.

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Analysis, 4th edn √ 25 + 16 (b) √ √ x· 4=4 (e) 22−x = 8 √ ? 5 4. Rationalize the denominator and simplify: SM ⊂ ⊃ 5. 6 (a) √ 7 √ 32 (b) √ 2 √ 3 (c) √ 4 2 2 (e) √ √ 3 8 4 (f) √ 2y x (g) √ 2x / FRACTIONAL POWERS 23 √ √ 54 − 24 (d) √ 6 √ x x+1 (h) √ x Simplify the following expressions by making the denominators rational: √ √ x 5− 3 1 (b) √ (c) √ (a) √ √ √ 3−2 7+ 5 5+ 3 √ √ √ x y−y x 1− x+1 h (f) (e) √ (d) √ √ √ √ x y+y x 1+ x+1 x+h− x 6. 008 (d) 7. 0001)10000 8. The population of a nation increased from 40 million to 60 million in 12 years.

2 1. Find the value of Y in the models (iii) and (iv) in Example 1. Verify that formula (∗∗) gives the same result. SM ⊃ 2. ⊂ Solve the following equations for x: 1 1 + =2 ax bx √ ax =0 (d) 1 + x + √ 1+x (a) (b) ax + b =A cx + d (c) (e) a 2 x 2 − b2 = 0 1 −1/2 px −w =0 2 (f) (3 + a 2 )x = 1 3. 14 for p (supply of rice in India) (b) S = α + βP for P (supply function) (c) A = 21 gh for g (the area of a triangle) (d) V = 43 πr 3 for r (the volume of a ball) (e) AK α Lβ = Y0 for L (production function) SM ⊂ ⊃ 4.

On the basis of the sign variations for p, p − 2, and p − 1, the sign variation for p(p − 2)/(p − 1) is determined. For example, if 0 < p < 1, then p is positive and (p − 2) is negative, so p(p − 2) is negative. But p − 1 is also negative on this interval, so p(p − 2)/(p − 1) is positive. Arguing this way for all the relevant intervals leads to the following sign diagram. (The original inequality has no meaning when p = 1. ) −1 p 0 1 3 ◦ ◦ p−2 p−1 p(p − 2) p−1 2 ◦ ◦ ∗ ◦ So the original inequality is satisﬁed if and only if 0 < p < 1 or p > 2.