Differential and Integral Calculus – Midterm – Fall 2024

Daffodil International University Department of Business Administration Course Title: Differentiation and Integral Calculus Course Code: 0541-214 Semester: Fall 2024 Time: 1 Ilour 30 minutes Section: All Examination: Midterm Term Full Marks: 25 Teachers' Initial: DMSA, Asmani, Ashad [NB: Answer all the following questions] 01 Ä Define domain and ran e ofa function Discuss marginal cost, mar inal revenue, and mar inal rofit 02 Sketch the ra h of the function 3 b) Justify the relation y = — is a function. Also find the domain and ran e. CLO 1, L 1 CLO 1, L 2 (CLO 2, L 3) (CLO 2, L 3) 2 3 2 3 dy 03 Find — a) b) 2 y = (5x + + 6xä + + 500 Y = e4X(1 + The gross domestic product (GDP) of a certain country was 04 = x2 + 5x + 106 billion dollars x ears after 2020.v At what rate was the GDP changing with respect to time in 2026? (CLO 2, L 3) 2.5 (CLO 2, L 3) 2.5 (CLO 2, L 3) 3 05 ) By how much will the GDP actually change during to the time (CLO 2, L 3) 2 in 2030? (CLO 2, L 3) 5 2 + 3x + 67 is the total cost of producing x units c(x) = of a particular commodity and p(x) = 9 — is the price at 5 which all x units will be sold. AsSume p(x) and C(x) are in dollars. Find the mar inal cost and the mar inal revenue. F) Use marginal cost to estimate the cost of producing the fourth unit. Find the actual cost of roducin the fourth unit. P) Use marginal revenue to estimate the revenue derived from the sale of the fourth unit. IF) Find the actual revenue derived from the sale of the fourth unit.