The contents, or parts thereof, may be reproduced in print form solely for classroom use with FUN... more The contents, or parts thereof, may be reproduced in print form solely for classroom use with FUNDAMENTAL METHODS OF MATHEMATICAL ECONOMICS provided such reproductions bear copyright notice, but may not be reproduced in any other form or for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. ISBN 0-07-286591-1 (CD-ROM) 3. No. When S 1 = S 2 . 4. Only (d) represents a function. 5. Range = {y | 8 ≤ y ≤ 32} 6. The range is the set of all nonpositive numbers. 7. (a) No. (b) Yes. 8. For each level of output, we should discard all the inefficient cost figures, and take the lowest cost figure as the total cost for that output level. This would establish the uniqueness as required by the definition of a function. Exercise 2.5 1. N/a 2. Eqs. (a) and (b) differ in the sign of the coefficient of x; a positive (negative) sign means an upward (downward) slope. Eqs. (a) and (c) differ in the constant terms; a larger constant means a higher vertical intercept. 3. A negative coefficient (say, -1) for the x 2 term is associated with a hill. as the value of x is steadily increased or reduced, the −x 2 term will exert a more dominant influence in determining the value of y. Being negative, this term serves to pull down the y values at the two extreme ends of the curve. 4. If negative values can occur there will appear in quadrant III a curve which is the mirror image of the one in quadrant I. 5. (a) x 19 (b) x a+b+c (c) (xyz) 3 6. (a) x 6 (b) x 1/6 7. By Rules VI and V, we can successively write x m/n =(x m ) 1/n = n √ x m ;b yth esam et w or ule s, we also have x m/n =(x 1/n ) m =( n √ x) m 8. Rule VI: (x m ) n = x m × x m × ... × x m | {z } nt e r m s
The contents, or parts thereof, may be reproduced in print form solely for classroom use with FUN... more The contents, or parts thereof, may be reproduced in print form solely for classroom use with FUNDAMENTAL METHODS OF MATHEMATICAL ECONOMICS provided such reproductions bear copyright notice, but may not be reproduced in any other form or for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. ISBN 0-07-286591-1 (CD-ROM) 3. No. When S 1 = S 2 . 4. Only (d) represents a function. 5. Range = {y | 8 ≤ y ≤ 32} 6. The range is the set of all nonpositive numbers. 7. (a) No. (b) Yes. 8. For each level of output, we should discard all the inefficient cost figures, and take the lowest cost figure as the total cost for that output level. This would establish the uniqueness as required by the definition of a function. Exercise 2.5 1. N/a 2. Eqs. (a) and (b) differ in the sign of the coefficient of x; a positive (negative) sign means an upward (downward) slope. Eqs. (a) and (c) differ in the constant terms; a larger constant means a higher vertical intercept. 3. A negative coefficient (say, -1) for the x 2 term is associated with a hill. as the value of x is steadily increased or reduced, the −x 2 term will exert a more dominant influence in determining the value of y. Being negative, this term serves to pull down the y values at the two extreme ends of the curve. 4. If negative values can occur there will appear in quadrant III a curve which is the mirror image of the one in quadrant I. 5. (a) x 19 (b) x a+b+c (c) (xyz) 3 6. (a) x 6 (b) x 1/6 7. By Rules VI and V, we can successively write x m/n =(x m ) 1/n = n √ x m ;b yth esam et w or ule s, we also have x m/n =(x 1/n ) m =( n √ x) m 8. Rule VI: (x m ) n = x m × x m × ... × x m | {z } nt e r m s
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