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: 2304 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 ln x x Question 1. (L.O.2) Let F (x) be an antiderivative of the function √ , satisfying F (1) = 3 −2.25. Which of the following statements is true? A. All other statements are wrong. B. lim+ F (x) = 1 C. lim+ F (x) = 0 D. lim+ F (x) = +∞ x→0 x→0 x→0 Question 2. (L.O.2) Given the function y = y(x) defined by the parametric equation x = sin t − 2t, y = 2 (1 − cos(2t)) . On which  π of the following intervals  π 3π  is this function  decreasing?  π π A. − , , B. C. 0, 4 4 2 4 4  3π 5π  D. 4 , arcsin2 x Question 3. (L.O.2) Let F (x) be a function satisfying F ′ (x) = √ 1 − x2 4 . Given that lim F (x) = 0. Find F (−0.9) x→1− A. −1.7599 B. −1.2319 C. −1.0559 D. −2.1119 Question 4. Find all values of a such that Z∞ (x + 1)eax dx = 2 0 A. a = 1/2 C. a = −1 B. a does not exist D. a = −1 or a = 1/2 Question 5. (L.O.2) Let y = f (x) be a function whose graph is shown in the figure below. Page 1/4 Code 2304 y y = f (x) Let g(x) = f (t) d t. Given that the areas of regions 1, 2 and 3 are 1.3, 3.5 and 9.6, −10 respectively. Find the maximum value of g(x), where −10 ≤ x ≤ 2. A. −6.1 B. None of the others C. −7.4 D. 1.5 Question 6. (L.O.1) Use the central R