Mathematics Assignment 1 (2024-25) PDF

Summary

This document is an assignment related to mathematics, specifically covering sequences, series, and calculus concepts. It includes questions on topics like implicit and explicit functions, oscillatory series, and improper integrals.

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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

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