Mathematics Assignment 1 (2024-25) PDF

CHANDIGARH ENGINEERING COLLEGE-CGC Department of Applied Sciences Assignment No 1 Max. Marks: 30 Subject and...

CHANDIGARH ENGINEERING COLLEGE-CGC Department of Applied Sciences Assignment No 1 Max. Marks: 30 Subject and Subject code: Mathematics –I/ BTAM--101-23 Semester 𝟏𝒔𝒕 (CSE/IT/AI-DS/AI-ML/IOT/DS/ECE/ME/RAI/E&CE) Date on which assignment given: 13/08/2024 Date of submission of assignment: 28/08/2024 Course Outcomes: Students will be able to: CO1 Examine the convergence and divergence of sequences and series. Apply the concept of Proper integral to find length , surface area and volume of revolution of the CO2 curves and to deal with discontinuous functions using Improper integral. Use the concepts of partial differentiation to expand , estimate and find the extreme values of CO3 Multivariable Functions. CO4 Evaluate area and volume of the surfaces using the concept of double and triple integration. Bloom’s Taxonomy Levels L1 – Remembering, L2 – Understanding, L3 – Applying, L4 – Analysing, L5 – Evaluating, L6 - Creating Bloom’s Relevance to Assignment related to COs Taxonomy CO No. Level SECTION - A (2Marks Each) Q1. Explain the concept of Implicit and Explicit functions. L-2 CO-3 Q2. Define Oscillatory series with an example. L-1 CO-1  Show that the geometric series ∑∞ 𝑛 𝑛=0 𝑟 , where r is any real number such Q3. that L-3 CO-1 |r| 0 L-4 CO-1 1.2 3.4 5.6 𝑥+𝑦 𝜕2𝑢 𝜕2𝑢 𝜕 2𝑢 sin 𝑢𝑐𝑜𝑠2𝑢 L-5 CO-3 Q7. If 𝑢 = sin−1 , prove that 𝑥 2 𝜕𝑥 2+2𝑥𝑦 𝜕𝑥𝜕𝑦 + 𝜕𝑦 2= - √𝑥+√ 𝑦 4𝑐𝑜𝑠 3 𝑢 2 2 2 𝜕2 𝑢 𝜕2 𝑢 ′′ ( ) ′ 1 Q8. If u=f(r) where 𝑟 = 𝑥 + 𝑦 , show that𝜕𝑥 2 +𝜕𝑦 2=𝑓 𝑟 + 𝑟 𝑓 (𝑟) L-4 CO-3 A rectangular box open at the top, is to have volume of 32 cubic metres. Find Q9. the dimensions of the box requiring least material for its construction. L-5 CO-3 Test whether the series is conditionally convergent or not Q10. ∞ L-6 CO-1 (−1)𝑛−1 𝑛 ∑ 2 𝑛 +1 𝑛=1