DEC 2016 , BOOKLET B, Ques NO. 32

Ques: A function f :  R^2 -> R is defined by f(x,y) = xy. Let V =(1,2) and a = (a1,a2) be two elements of R^2. The directional derivative of f in the direction of v at a is
1.  a1 + 2a2
2. a2 + 2a1
3. a2/2 + a1
4.  a1/2 +a2
Solution:

Real Analysis Solutions (Uniform Continuity -1)

Some examples of uniformly continuous and non uniformly continuous functions on (0,1)

Uniformly continuous functions
 

•  e^x 
•  sin(x)
•  cos(x) 
• x sin(1/x)
•  (sin x)/x 
• x

Non uniformly continuous functions

•  tan(πx/2) 
•  sin(1/x)
•  (cos x)/x
• 1/x

Real analysis solutions( LImit Part-1) - Csir Net Mathematics

2014 June, Real Analysis, Limit

                                 
                                                  

        

Real analysis solutions - Csir Net Mathematics

2014 June, Real Analysis, Limit

                                 
                                                  

        

Dec 2016 , Ques No. 72 , booklet B ( Linear Algebra)

Dec 2016, Ques. No. 69 booklet B ( linear algebra)