Lovely Professional University 2010 B.Tech Electronics and Communications Engineering Assignment 01 - exam paper

HOME WORK: I

School: Department: Mathematics

Name of the faculty member: Course No:MTH101

Course Title: Engineering Mathematics-I

Class:B.tech Term:I Section:C4001 Batch:2010

Max. Marks:25 Date of Allotment:14/08/10 Date of Submission:27/08/10

Part-A

Q1 (a) Evaluate the following limit ,

(b) Is the function when and continuous at origin? Redefine if necessary to make it continuous at(0,0).

Q2. Prove that satisfies the wave equation where c is a constant. Verify this when .

Q3. (a) Find if .

(b)Find the rate at which the area of a rectangle is increasing at a given instant when the sides of the rectangle are 4 ft and 3 ft and are increasing at the rate of 1.5 ft/sec and 0.5 ft/sec respectively.

Part-B

Q4. (a) Prove that if .

(b) Change the Laplace Equation in Cartesian coordinates into polar coordinates.

Q5. (a) Find when .

(b) If show thatand .

Q6. (a) If and , find .

(b)If ,,, find .