Engineering Calculus Tutorial Sheet 1 - EMAT101L 2024-25 - PDF

Course Name: Engineering Calculus Course Code: EMAT101L Academic Year: 2024-25 Semester: Odd Date: August 19, 2024 Type: 3-1-0 Tutorial Sheet: 1...

Course Name: Engineering Calculus Course Code: EMAT101L Academic Year: 2024-25 Semester: Odd Date: August 19, 2024 Type: 3-1-0 Tutorial Sheet: 1 CO-mapping: CO1 CO2 CO3 CO4 CO5 CO6 Q1 ✓ Q2 ✓ Q3 ✓ Q4 ✓ Q5 ✓ Q6 ✓ Q7 ✓ Objectives: Students will be able to understand Real number systems, Sets, Relations, and functions, bounded above, bounded below and bounded sets, maximum, minimum, supremum, infimum of a set, etc. 1. What is the number of subsets of a set containing five elements? 2. If | A |= 50, | A ∩ B |= 44 and | B |= 58 then what is | P (A − B) |? 3. In a survey of 1,00 consumers, it was found that 72 consumers liked product A and 45 liked product B. What is the least number that must have liked both the products? 4. If (x2 − 4x + 5, y 2 –63) = (x2 + 1, 1). Then find the values of x and y. 1 5. Let f : R → R be defined by f (x) = x ∀x ∈ R Then f is: (i) Injective (ii) Surjective (iii) Bijective (iv) Not defined. 6. Let f : R → R. Find the domain and range of the following functions: 5 3 √ √ (i) 9−x 2 (ii) √x−5 (iii) 16 − x2 (iv) x2 − x − 110 (v) cos(x) − 3.  7. Find the maximum, minimum, supremum, and infimum of the below mentioned sets. Besides, mention whether the set is bounded above, bounded below or bounded. n1 o (a) S1 = :n∈N n n (−1)n o (b) S3 = :n∈N n n o 2 (c) S5 = x ∈ R : x < 1 n o 2 (d) S6 = x ∈ R : x − 3x + 2 < 0 n o (e) S7 = x ∈ R : x2 − 3x + 2 > 0 n o (f) S8 = x ∈ Q : x2 − 2 ≤ 0 , where Q is the set of rational numbers. n1 1 o (g) S9 = + : m, n ∈ N m n n 1 o (h) S10 = (−1)m + : m, n ∈ N n In the above questions, check whether the supremum and the infimum of the set belongs to that set or not. “Live as if you were to die tomorrow. Learn as if you were to live forever.” —– Mahatma Gandhi 2