Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. The equation 4x - 3y = 12 describes a line in _3. b. The equation z2 = 2x2 - 6y2 determines z as a single function of x and y. c. If f has continuous partial derivatives of all orders, then fxxy = fyyx. d. Given the surface z = f 1x, y2, the gradient _f 1a, b2 lies in the plane tangent to the surface at 1a, b, f 1a, b22. e. There is always a plane orthogonal to both of two distinct intersecting planes.
Reading notes – Clifford, The Ethics of Belief (March 8) “When an action is once done, it is right or wrong for ever; no accidental failure of its good or evil fruits can possibly alter that.” Question of right or wrong origin of belief Man always has chance to act on what evidence suggests. No person with beliefs can be unbiased “No man holding a strong belief on one side of a question, or even wishing to hold a belief on one side, can investigate it with such fairness and completeness as if he were really in doubt and unbiased.” If beliefs are not stored immediately after experience, they are used for future guidance. “An awful privilege or an awful responsibility, that we should help to crea