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Real Analysis
If f(x,y) = {1 if (x,y) = (0,0)
sin(x,y) if (x,y)#(0,0).find lim(x,y) converges to (0,0) f(x,y)
sin(x,y) if (x,y)#(0,0).find lim(x,y) converges to (0,0) f(x,y)
Real Analysis
If fn converges to f and FN is bounded on a set S prove that {fn} is uniformly bounded on S
Real Analysis
Determine which of the following functions are of bounded variation on[0,1]
a. f(x)= x^2sin(1/X) if x#0 ,f(0)=0
b. f(x)= √x sinx,if x#0,f(0)=0
a. f(x)= x^2sin(1/X) if x#0 ,f(0)=0
b. f(x)= √x sinx,if x#0,f(0)=0
Real Analysis
If f:R^2 to R defined by f(X,y) ={x^2y^3/x^4+y^2. if (x,y)#(0,0)
0 if (X,y) =(0,0). Find the directional derivative of f(X,y) at (0,0)?
0 if (X,y) =(0,0). Find the directional derivative of f(X,y) at (0,0)?
Real Analysis
Prove that an open interval in R is an open set and a closed intervals is a closed set
Real Analysis
Find limit of sequence =n+2/3-n
Real Analysis
If f(X,y)={xy/x2+y2, if(X,y)#(0,0)
0 if (X,y)=(0,0)
Check the continuity CF F(X,y) at (0,0)
0 if (X,y)=(0,0)
Check the continuity CF F(X,y) at (0,0)
Real Analysis
Prove that lim(Xn) =0 iff lim(|Xn|)=0 . Give an example to show that convergence of (|Xn|) need not imply the convergence of (Xn)
Real Analysis
With the help of sequences, calculate √5 correct upto 5 decimals.
Real Analysis
Show that if X and Y are sequences such that X and X + Y are convergent, then Y is convergent.
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#339914 on Dec 2023
#339914 on Dec 2023