Cambridge University Planes and Vectors & Limits and Domains Questionnaire

Cambridge University Planes and Vectors & Limits and Domains Questionnaire

Planes and Vectors, Limits and Domains

 

Let P denote the plane given by the point-normal equation () = = (1, 2, -1)·((x, y, z) – (1, 1, 1)) and L denote the line given by the vector equation (x, y, z) = (1,0, 2) + t(2, 1,4), teR. Which of the following geometrically describes the intersection of L and P ? (a) A plane in R3 (c) The empty set (b) A line in R3 (d) A single point in R3 Consider a real number a and a function f on its natural domain D. Which of the following statements about the function f are true? Statement A: If lim f(x) exists and is a real number, then a € D Statement B: If lim f(x) exists and is a real number, then f is continuous at the point x = a. — (a) B only (c) Neither A nor B (b) Both A and B (d) A only
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