Exercises 49–53 involve Definition 2.2 of the limit.
In this problem, you will establish rigorously that
(a) Show that |x| ≤ ||(x, y)|| and |y| ≤ ||(x, y)||.
(b) Show that |x3 + y3| ≤ 2(x2 + y2)3/2. (Hint: Begin with the triangle inequality, and then use part (a).)
(c) Show that if 0<||(x, y)||<δ, then |(x3 + y3)/ (x2 + y2)| < 2δ.
(d) Now prove that lim(x,y)→(0,0)(x3 + y3)/(x2 + y2) = 0.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.