Economics 207 Laboratory Exercise 5 - Fall 2006, Lab Reports of Economics

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ECONOMICS 207

FALL 2006

LABORATORY EXERCISE 5

Problem 1. Solve the following equations for x. (i) (^) x+2^3 (^) x^1 = (^51) x

(ii) x^2 + 4bx 3 x 12 b = 0

(iii) Ax = c

Date: 19 September 2006. 1

Problem 2. Solve the following systems of equations for x 1 , x 2 , and/or x 3 using the method of substitution and in part b, also use the method of elimination. (i) 3 K^

(^34) L^

(^57)

1 2

K

1 (^4) L 2 (^7) =

(ii) x 1 + 2x 2 + x 3 = 3 x 1 + 2x 2 + 2x 3 = 2 x 1 + 3x 2 x 3 =

Problem 4. Find the derivatives of each of the following functions with respect to x. (i) f (x) = (7x + 3)(2x^2 4) Show two ways.

(ii) f (x) = 11x^2 e^2 x

(^2) 3 x

(iii) f (x) = ln[(x^4 + 3x^2 )^2 ]

(iv) f (x) = ln(x

(^2) ax) bxe^3 x

Problem 5. For each of the following, take the derivative with respect to x 1 , set the derivative equal to zero and solve the resulting equation for x 1.

(i) f (x 1 ) = 72px

(^14) 1 ^4 x^1

(ii) f (x 1 ; x 2 ) = 36x

(^16) 1 x^

(^13) 2 ^6 x^1