京都大学情報学研究科知能情報学専攻 2024年2月実施専門科目 F1-2

Author

Consider the following functions and .

(1) Evaluate whether and are differentiable, respectively. (2) Evaluate whether their derivatives and are continuous at , respectively.

Evaluate the directional differentiability and continuity of the following function.

Compute the volume in the -space for each of the following conditions.

(1) Under the surface and over the rectangle defined by on the -plane. (2) Under the surface of the paraboloid and over the -plane.