PG entrance exam IIT JAM 2025 Mock Test Mathematical Science Analysis Functions of Several Variables
Let f : ℝ3 → ℝ be defined as f(x, y, z) = x3 + y3 + z3, and let L : ℝ3 → ℝ be the linear map satisfying
\(\rm \displaystyle\lim_{(x,y, z) \rightarrow (0,0,0)}\) \(\rm\frac{f(1+x, 1+y, 1+z)-f(1,1,1)-L(x, y, z)}{\sqrt{x^2+y^2+z^2}}\) = 0
Then L(1, 2, 4) is equal to ________. (rounded off to two decimal places)
Enter numerical value using the virtual keypad. Round off where necessary.