Another Non-Differentiable Surface
Nguồn: http://clem.mscd.edu
Người gửi: Nguyễn Thị Ánh Nguyệt (trang riêng)
Ngày gửi: 16h:39' 25-10-2007
Dung lượng: 244.7 KB
Số lượt tải: 9
Mô tả: The surface f[x, y] = x^3/(x^2 + y^2) is also continuous at the origin and both of the first order partial derivatives are defined there. In fact, this surface has directional derivatives in every direction at the origin. (That is, each of the curves in which the surface intersects a plane contining the z-axis has a tangent line at the origin.) Nevertheless, the function is not differentiable there. (The surface has no tangent plane at the origin.)
Người gửi: Nguyễn Thị Ánh Nguyệt (trang riêng)
Ngày gửi: 16h:39' 25-10-2007
Dung lượng: 244.7 KB
Số lượt tải: 9
Mô tả: The surface f[x, y] = x^3/(x^2 + y^2) is also continuous at the origin and both of the first order partial derivatives are defined there. In fact, this surface has directional derivatives in every direction at the origin. (That is, each of the curves in which the surface intersects a plane contining the z-axis has a tangent line at the origin.) Nevertheless, the function is not differentiable there. (The surface has no tangent plane at the origin.)
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