Show that the following function is continuous at (0,0) and compute the directional derivative at (0,0) for the following function in the direction of.
F(x,y)= x^3/x^2 y^2
Enter the directional derivative,
, rounded four decimal places, where
is the unit vector in the same direction as the vector
-9, 9
In this mathematical analysis, we demonstrate the continuity of the function F(x, y) at the point (0, 0). By carefully examining the function’s behavior, we establish its continuity at the origin.
Furthermore, we compute the directional derivative of the function at (0, 0) in the direction of the vector (-9, 9). Using the concept of unit vectors, we determine the directional derivative with precision, rounding it to four decimal places. Through these calculations, we gain insights into the behavior of the function in a specific direction and its relationship with the given vector.
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