L24 Math 233 Lecture Notes - Lecture 19: Level Set, Nissan L Engine, Unit Vector
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L24 math 233 lecture 19- applications of the gradient vector. Recall: then f(x,y) is continuous at every point in the plane. 0 + h y0 + h f. )]/h h 0: this limit exists for every unit vector u. Look at the level curves of this equation in the xy plane at x2 + y2 = 1. This will give a circle with radius 1 centered around the origin. , the gradient vector points in the direction of of fastest increase which is. Moving along the circle gives a constant value (1) Direction of fastest increase is perpendicular to any point on the circle. 0 y0 f(x , k = f (x , This is useful for drawing level curves is normal (perpendicular/orthogonal) to the tangent line to the level curve for. This idea works in higher dimensions as well. Example 2: suppose f(x,y,z) is differentiable in 3 dimensions.
