7 + 5 ? 1 x (7 + 5) 4 DO 1 2 4 5 6 7 8 9 Enter v II

Question 2. functions f : [0, 1] → R. Define an integral norm || - ||i by Let C[0, 1] represent the collection of continuous ||f||: := / \f(x)| dx. 0. We then introduce a distance function p which is given in terms of the integral norm || · Ili as P(f,9) := ||f – 9|li, Vf, g€ C[0, 1] To show that is a metric space: (a) Prove that the distance function p positive definite on C[0, 1]. (b) Is the distance function p is symmetric? Justify. (c) Show that p satisfies the triangle inequality on C[0, 1]. (d) Conclude whether or not is a metric space. Would you say that it is a complete metric space or not? Justify your answer.

Consider the following. x = sin(t), y = csc(t), 0st< T/2 (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. y y -1 4 X 1 y y X 6 5

72+(236+4/5x4) divide 4-5