(a) For the limit limx 1 (x3 x 1) 3, use a graph to find a value of that corresponds to 0 4 (b) By using a computer algebra system to solve the cubic equation x3 x 1 3 , find the largest possible value of that works for any given 0 (c) Put 0 4 in your answer to part (b) and compare with your answer...

a The points of intersection in the graph are x 1 26 and x 2 34 with x 1 0 ...

(a) For the limit limx 1 (x3 + x + 1) = 3, use a graph to...

Question:

(a) For the limit limx →1 (x3 + x + 1) = 3, use a graph to find a value of δ that corresponds to ε = 0.4.
(b) By using a computer algebra system to solve the cubic equation x3 + x + 1 = 3 + ε, find the largest possible value of that works for any given ε > 0.
(c) Put ε = 0.4 in your answer to part (b) and compare with your answer to part (a).