Question

1. true or false: (a) closer contour curves means that the function is changing more slowly than where the curves are further apart. (b) if a function is continuous on every line that passes through the origin, then it is continuous at the origin.

Explanation:

(a) Closer contour curves mean the function is changing more rapidly, not more slowly. So this statement is false.
(b) Just because a function is continuous on every line passing through the origin doesn't mean it is continuous at the origin. There could be non - linear paths approaching the origin where the function is discontinuous. So this statement is false.

Answer:

(a) False
(b) False