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(a) 5x-3 – 4 (i) Lim x-00 2x-2 + 9 (x – 3)2 (ii) Lim x-00 X00 x2 7- 2x – 3 2

(a) 5x-3 – 4 (i) Lim x-00 2x-2 + 9 (x – 3)2 (ii) Lim x-00 X00 x2 7- 2x – 3 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 4 (a) 5x-3 – 4 (i) Lim- x-00 2x-2 +9 (х — 3)2 (ii) Lim X00 x2 2 - 2x – 3 (b) During a nationwide program to immunize the population against a new strain of the flu, public health officials determined that the cost of inoculating x% of the susceptible population 1.85x would be approximately C(x) = million dollars. 100 – x (i) What would it cost to providing immunization to the first 20% of the susceptible population? (ii) What would it cost to providing immunization to the next 30% of the susceptible population? (iii) Suppose 17 million dollars are available for providing immunization. What percentage of the susceptible population will not receive immunization? (iv) If money was not a problem will they be able to providing immunization to the entire susceptible population? (2x² – 4 (c) Determine the values of x for which the function f(x) = }x + 2 x < 2 2 < x > 5 x 2 5 7 is discontinuous.
Transcribed Image Text:Problem 4 (a) 5x-3 – 4 (i) Lim- x-00 2x-2 +9 (х — 3)2 (ii) Lim X00 x2 2 - 2x – 3 (b) During a nationwide program to immunize the population against a new strain of the flu, public health officials determined that the cost of inoculating x% of the susceptible population 1.85x would be approximately C(x) = million dollars. 100 – x (i) What would it cost to providing immunization to the first 20% of the susceptible population? (ii) What would it cost to providing immunization to the next 30% of the susceptible population? (iii) Suppose 17 million dollars are available for providing immunization. What percentage of the susceptible population will not receive immunization? (iv) If money was not a problem will they be able to providing immunization to the entire susceptible population? (2x² – 4 (c) Determine the values of x for which the function f(x) = }x + 2 x < 2 2 < x > 5 x 2 5 7 is discontinuous.
Problem 1 (a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. (i) Derive an expression, R(q) for Teddy J's total revenue curve. (ii) Derive an expression, I(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid. (iv) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profits. (b) A firm has an average cost function 125 A(q) - 4. 16 where q is the firm's output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible? (iv) Write an equation for the total cost function. (v) Hence calculate the level of output for which total costs are minimum.
Transcribed Image Text:Problem 1 (a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. (i) Derive an expression, R(q) for Teddy J's total revenue curve. (ii) Derive an expression, I(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid. (iv) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profits. (b) A firm has an average cost function 125 A(q) - 4. 16 where q is the firm's output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible? (iv) Write an equation for the total cost function. (v) Hence calculate the level of output for which total costs are minimum.
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