Question

(2 points) 1 equals The result from class that says that if A upper triangular and is partitioned as then 1,1-를4,1 41,2 0 1,111,2 where A1,2 is all the entries of the last column except for the element d In this problem, use the above method to successively find the values in each column from A1 6 0 -18 6 6 0 4 -12 4 16 1. Let A0 0 4 412 then Abl b2 b3 b4 b5] 0 0 0 5 10 0 0 00 2 75 4 2 75 25 125 b3-25 where b10 b20 .2

Answer 1

f(x,y) = x^4/x^4 + y^2 we have to find lim_(x,y) rightarrow (0,0) x^4/x^4 + y^2 does not exists let y = k x^2 and x notequalto 0 Then f(x,y) = x^4/x^4 + (kx^2)^2 = x^4/x^4 + k^2 x4 = x^4/x^4 (1 + k^2) = 1/1 + k^2 Suppose (x,y) approaches (0,0) along the curve k = 1 Then f(x,y) = 1/1 + 1 = 1/2 so lim_(x,y) rightarrow (0,0) f(x,y) = lim_(x,y) rightarrow (0,0) 1/2 = 1/2 If (x,y) approaches (0,0) along the curve when k = 0 Then (x,y) = 1/1 + 0 = 1 so lim_(x,y) rightarrow (0,0) f(x,y) = lim_(x,y) rightarrow (0,0) 1 = 1 Hence limit does not exists at f has different limit along different paths