ū=3,p, 2. For and v=(-9,12,p) determine the value of p when a) û and are collinear 3. Given 171=5 151=12 |+5|=13 and determine the value of 21-357 +5

1. Integral of [ ln (sqrt (x^3+4)) ] dx
2. Integral of [ (x^2)(cos(x)) ] dx

Find the derivative of f(x)=105?x3??x7+63?x8?3

Determine whether Rolle’s Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle’s Theorem. g(x) = x2 + 9×2 +24x + 16; (-4. – 1] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Rolle’s Theorem applies and the point(s) guaranteed to exist is/are x= (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) O B. Rolle’s Theorem does not apply. a. Determine whether the Mean Value Theorem applies to the function f(x) = In 7x on the given interval [1, e]. b. If so, find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem. a. The Mean Value Theorem to the function b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The point(s) is/are x = (Type an exact answer. Use a comma to separate answers as needed.) B. The Mean Value Theorem does not apply in this case. Use the figures to calculate the left and right Riemann sums for f on the given interval and the given value of n. a $(x) = -2 2 o f(x) = +2 on (1,5); n = 4 V* 0 2 3 4 5 0 2 3 4 ch- The left Riemann sum for fis (Round to two decimal places as needed.) The right Riemann sum for fis (Round to two decimal places as needed.) Evaluate the following definite integral using the Fundamental Theorem of Calculus. In 4 5 exdx 9 0 In 4 9 I e*dx= [ (Type an integer or a simplified fraction.) 0 Use a change of variables or the table to evaluate the following indefinite integral. [2x6x2 + 16) ºd Click the icon to view the table of general integration formulas. [2x(x2 +16) *dx=

Sultanate of Oman Ministry of Manpower Directorate General of Technological Education Al Musanna College of Technology Business Engineering ✓ IT ELC Final Assignment – Student Answer Sheet Semester II, Academic Year 2019-20 Student ID Section Student Name Number of Pages Email-id Mobile Number Course Code & Name Specialization Assignment Available Date Assignment Due Date MATH1200 & Calculus I IT / ENGG 17-05-2020 10:00 a.m. 19-05-2020 10:00 a.m. Level Diploma Duration 48 hours Mode of Exam Online submission INSTRUCTIONS TO CANDIDATES As part of the statement issued by the Board of Trustees of the Colleges of Technology and in compliance with the Order issued by the Supreme Committee for dealing with the development of the COVID-19 pandemic, ACT has transitioned to online platforms for conducting Final Assignment (replacing the Final Exam) for relevant courses. • Fill in the above details. • Final Assignment questions are available in your eLearning course page as per Final Assignment Timetable. • Provide answers for the questions in this answer sheet. • You will get a maximum of 48 hours to submit the assignment. • Clarifications / Discussions on assignment with lecturers is not permitted. • Completed answer sheets (MS Word Document/PDF) should be submitted via eLearning or other means as instructed. • Any Assignment submitted after 48 hours from the scheduled date will be considered as a late submission and a penalty will be applied that results in the mark being reduced to zero. • Technical issues, if any, should be immediately notified to the Department through the following focal points. IT – Mr. Faheem Ahmed (faheem@act.edu.om) Engg – Mr. AbdulHamid Al Hinai (alhinai@act.edu.om) • Math – Ms.Mini Punnoli (mini@act.edu.om) BS – Mr. Jaffer Ali Khan (jaffer@act.edu.om) Copying or cheating or malpractices of any kind are strictly prohibited. Violations will be promptly reported to higher authorities, and serious actions will be taken according to the ‘Article 80, Bylaws of Colleges of Technology’, issued by Ministry of Manpower, Sultanate of Oman. FOR VALUATION PURPOSE ONLY Section A B C D E Total Marks Marks Allocated Marks Scored 10 10 10 10 10 50 Marked by __________________ Signature ______________________ _________ 50 Date ________ Page 1 of 8 Student Declaration Semester II, Academic Year 2019-20 To, The Head, Department of Business/Engineering/IT I, (Student’s Name) …………………….…………………………………….……………, (Student’s ID): …………………….., Student of Diploma / Adv. Diploma / B. Tech Level, in ……………… Section of Business / Engineering / IT Department, hereby declare that my submission of Final Assignment as requirements for the Course Name…………………………………. Course Code ……………………………… are results of my own original work except for source materials explicitly acknowledged by proper citations. I also understand that plagiarism is an offense that can lead to disciplinary action depending on the seriousness of the case. Signature : Name : Date : (Extracted from QD_ Plagiarism Policy V2.2) Page 2 of 8 SECTION A Question Type your answers against the question number. No. ________ 10 Marks Individual Marks Scored Page 3 of 8 SECTION B Question Type your answers against the question number. No. ________ 10 Marks Individual Marks Scored Page 4 of 8 SECTION C Question Type your answers against the question number. No. ________ 10 Marks Individual Marks Scored Page 5 of 8 SECTION D Question Type your answers against the question number. No. ________ 10 Marks Individual Marks Scored Page 6 of 8 SECTION E Question Type your answers against the question number. No. ________ 10 Marks Individual Marks Scored Page 7 of 8 Page 8 of 8 WIN A3.1. Given a function 3×2 + 4x – 4. x = 3x – 2 g(x) = 8 2 X = 3′ 3 Check whether it is continuous at 2 X = and justify your answer with 3 necessary steps. – 2 [5 Marks] 5 X – x+4 A3.2. Evaluate lim x1 x – 1 [5 Marks] Question 4 Answer saved Marked out of 10.0 P Flag question D3.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 3×2 + 2x – 13 at a = -2. [4 Marks] D3.2. (a) Find the derivative of y = 4 tan( V1 + Vx). (b) If y = sin(tan(cos(x2 + 3x + 2))), then find the first derivative. [3 Marks] D3.3. Using logarithmic differentiation, find the derivative of y = (sec x + 1)+? [3 Marks] Question 5 Incomplete answer Marked out of 10.0 P Flag question E3.1. The position in feet of a motor bike along a straight track after t seconds is modelled by the function s(t) = 3t2 – 4t – 3. Calculate the “average velocity” of the bike over the time interval [3, 3.2] and also determine its instantaneous velocity at time t = 4 seconds. [4 Marks] E3.2. Find the critical points for the function f(x) = x3 – 6×2 + V3. .3. If y = = tan O n(). [3 Marks] dy then find dx3 [3 Marks] Question 2 Answer saved Marked out of 10.0 Flag question B2.1. Explain the three conditions of continuity and draw a graph of some function for which the limit exists at x = 3. Also, the function should be defined and discontinuous at x = 3. [4 Marks] B2.2. In the table below, the values of functions h(t), k(t) and their derivatives h’ (t) and k’ (t) at t = 5 are given as follows: t 5 1 h(t) k(t) -3 h’ (t) 3 k’ (t) 7 Find the value of (h(t) · k(t)) at dt t = 5. [3 Marks] B2.3. Find the derivative of the function using quotient rule: 3 sint 412 s(t) = + t5 cott [3 Marks] Question 3 Answer saved Marked out of 10.0 P Flag question C1.1. If x = 3t + sin at and y = 2t – cos at , then find the dạy second derivative using dx2 parametric differentiation. [5 Marks] C1.2. Find the “equation of normal to the tangent” at the point (2, -1) for the curve 2y + 5 – x2 – y2 = 0. [5 Marks]