Lecturer: Huỳnh Thị Hồng Diễm . . . ........................................... ........................................... Approved by: Lê Xuân Đại . . . . . . . . . ........................................... ........................................... ........................................... ........................................... Semester/Academic year I 2025-2026 Date 23/12/2025 Course title: Calculus 1 UNIVERSITY OF Course ID: MT1003 TECHNOLOGY Duration: 70 Mins Code: 2303 Faculty of AS Notes: - You are NOT allowed to use materials. Each correct answer is awarded 10/22 points. Each incorrect answer is deducted by 25% of correct answer. Answers left blank will not be counted. Do not round between steps. Round your final answers to 4 decimal places. Final Exam x Question 1. (L.O.1) Calculate the average value of f (x) = 2 , where −1 ≤ x ≤ 2. x +1 A. −0.0333 B. −0.05 C. 0.4581 D. 0.1527   t Question 2. (L.O.2) Let f (x) = 10 1 − e− 3 . Find f −1 (9). 9  11  9 A. −3 ln B. − ln C. 3 ln D. 3 ln(10) 10 10 10 Question 3. (L.O.1) Let f (x) be a function satisfying f (6.3) = 6.7, f ′ (6.3) = 5. Using the linear approximation to estimate the value of f (5.985), we obtain A. 5.1250 B. 2.8895 C. 8.275 D. 7.1105 Question 4. The shape of a fountain pond is shown in the figure below. Assuming the thickness of the walls and bottom of the pond is neglected, the volume of the pond is equal to the volume of the solid of revolution generated by revolving the region bounded by the −(x + 2)3 1 curve y = + , 2 coordinate axes and the line y = 1 about y -axis. Given that the 2 2 units on the coordinate axes are in meters (m), the volume of the pond is equal to A. 14.4513 m3 B. 13.8230 m3 C. 7.6296 m3 D. 16.9646 m3 Z 5x+4 p Question 5. (L.O.1) Let f (x) = t3 3 + t2 d t be a function. Find f ′ (−1). A. −2 B. 2 3 C. −10 D. 0 Question 6. (L.O.1) Find the general solution of the differential equation y ′ = x2 y 2 + 9x2 + 4y 2 + 36. Page 1/4 Code 230