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Final examination semester 2 academic year 2019-2020 course name Calculus 1 giúp các bạn học sinh có thêm tài liệu ôn tập, luyện tập nhằm nắm vững được những kiến thức, kĩ năng cơ bản, đồng thời vận dụng kiến thức để giải các bài tập một cách thuận lợi. | HCMC UNIVERSITY OF TECHNOLOGY AND FINAL EXAM SEMESTER 2 2019-2020 EDUCATION Subject Calculus 1 HIGH QUALITY TRAINING FACULTY Course code MATH141601E GROUP OF MATHEMATICS Number of pages 02 pages. ------------------------- Duration 90 minutes. Date of exam 31 07 2020 Materials are allowed during the exam. Question 1 1 point Given f x x 3 3 g x cos 2 x . a f x and g x are even odd or neither b Find f g x and g f x . Question 2 1.5 points a Find the value of the constant m such that the following piecewise - defined function is continuous everywhere. e3 x 1 x 0 f x x . m x 0 b With m found in question a find f x x. Question 3 1 point Let y be an implicit function of x satisfying the equation x 2 xy y 3 1 Find the tangent line to the graph of the equation at the point M 1 1 . Question 4 1 point Find the relative extrema of g x x 2 e 0.5 x . Question 5 1 point x 2 Let f x . Find the average value of f on the interval 0 1 . 4 x2 Question 6 1 point Find the particular solution of the separable differential equation dy y ln y 2x dx e satisfying the initial condition y 0 e. Question 7 1.5 points Assume that the position at time t of an object moving along a line is given by s t 2t 3 15t 2 36t for t on 1 4 . a Find the initial velocity and acceleration for the object. b When is the object advancing and retreating c When is the object accelerating and decelerating No. BM1 QT-PĐBCL-RĐTV Page 1 Question 8 1 point The volume of a spherical balloon is increasing at a constant rate of 10 cm3 s . At what rate is the radius of the balloon increasing when the radius is 3 cm Question 9 1 point A cylinder box Figure 1 is constructed with the volume V 24π cm3 . The cost of the material used for the bottom is 2 cm2 the cost of the material used for the lateral side is 2.5 cm2 and the cost of the material used for the top is 5 cm2. Find the dimension of the box r and h that minimizes the total cost. Notice Invigilators should not explain the questions on the exam papers. Expected .
