MATH 199 Calculus I Final Exam PDF 2018-2019
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Uploaded by ComplimentaryFreedom9345
Dhofar University
2019
Dhofar University
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Summary
This is a past paper for a Calculus I exam from Dhofar University, Spring 2018-2019. The exam covers topics such as limits, derivatives, and applications of these concepts. The questions include finding domains, limits of functions, and derivatives using definitions and implicit differentiation.
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(Vision for the Future) COLLEGE OF ARTS AND APPLIED SCIENCES (Department of Mathematics and Sciences) FINAL EXAMINATION QUESTION PAPER (Spring 2018-19) Course Code: MATH 199 Course Title: CALCULUS I Dat...
(Vision for the Future) COLLEGE OF ARTS AND APPLIED SCIENCES (Department of Mathematics and Sciences) FINAL EXAMINATION QUESTION PAPER (Spring 2018-19) Course Code: MATH 199 Course Title: CALCULUS I Date of Exam: 23-05-2019 Time: 09:00-11:00 Total Questions 9 Total Marks 40 Student Name Student ID Section 1&2 Note: - The question paper comprises of five (5) printed pages, including the cover page and the last page. If any page is missing, please inform the proctor immediately DEPARTMENT OF MATHEMATICS AND SCIENCES – MATH 199 FINAL EXAM - SPRING 2018-19 (Page 1 of 5) Useful Formulae d u u du e =e dx dx d 1 du ln u = dx u dx d u du a = a ln(a) u dx dx d 1 du log a u = dx u ln(a) dx d 1 du sin −1 u = dx 1 − u 2 dx d − 1 du cos−1 u = dx 1 − u 2 dx DEPARTMENT OF MATHEMATICS AND SCIENCES – MATH 199 FINAL EXAM - SPRING 2018-19 (Page 2 of 5) Answer All the following questions 1) Find the domain of the following function f ( x) = x − 16 [1 Mark] 2) Find the limits of the following functions 3x + 5 (a) lim ( 2 + x x →−1 3 ) [1 mark] x 2 − 7 x + 10 (b) lim ( ) [2 marks] x →2 x − 2 5x + 4 − 2 (c) lim ( x→0 x ) [3 marks] x 2 − 2 x + 2 sin 6 x (d) lim [3 marks] x →0 2 x cos x 3x 5 + x 2 + 1 (e) lim ( ) [2 marks] x→ x5 + 1 3) Consider the following function x + 3, x3 f ( x) = e ( 3− x ) , x3 6, x=3 Find (a) lim f ( x) + [1 Mark] x→ 3 (b) lim f ( x) − [1 Mark] x→ 3 (c) lim f ( x) x→3 [1 Mark] (d) Is f (x) continuous at x = 3 ? Give appropriate reason. [1 Mark] DEPARTMENT OF MATHEMATICS AND SCIENCES – MATH 199 FINAL EXAM - SPRING 2018-19 (Page 3 of 5) 4) Find the average rate of the change of the following function over the interval [-1,3]. [2 Marks] f ( x) = x 2 + 2 x 5) Using the definition, (a) Calculate the derivative of the following function at x = 1 [3 Marks] (b) Find the equation of the tangent line to the curve of the function at x = 1 [2 Marks] f ( x) = 2 x 2 − 3 6) Find the first derivatives of the following functions +1) f ( x) = 4( 2 x 2 (a) [2 Marks] (b) f ( x) = sin −1 (3x 3 + 2 x) [2 Marks] (c) f ( x) = e ( x 2 sin x ) [2 Marks] (d) f ( x) = ln( x 4 + 3 x 3 + 2 x) [2 Marks] 7) Use the implicit differentiation to find dy /dx of [2 marks] xy + y 2 = 1 DEPARTMENT OF MATHEMATICS AND SCIENCES – MATH 199 FINAL EXAM - SPRING 2018-19 (Page 4 of 5) 8) Use logarithmic differentiation to find dy /dx of [2 marks] y = (sin x) x x 3 3x 2 9) For the function , f ( x) = + − 18 x + 2 defined in the domain -∞ < x < ∞, find 3 2 (a) The critical points of f(x) [2 Marks] (b) The intervals where f(x) is increasing or decreasing [3 Marks] Intervals f’(x) Evaluated Sign of f’(x) Behavior of f(x) (Increasing or Decreasing) DEPARTMENT OF MATHEMATICS AND SCIENCES – MATH 199 FINAL EXAM - SPRING 2018-19 (Page 5 of 5)
