Questions from General Calculus

Q: Prove the statement using the ε, δ definition of a limit

Prove the statement using the ε, δ definition of a limit.

Q: Prove the statement using the ε, δ definition of a limit

Prove the statement using the ε, δ definition of a limit.

Q: Prove the statement using the ε, δ definition of a limit

Prove the statement using the ε, δ definition of a limit.

Q: Prove the statement using the ε, δ definition of a limit

Prove the statement using the ε, δ definition of a limit.

Q: Prove the statement using the ε, δ definition of a limit

Prove the statement using the ε, δ definition of a limit.

Q: Prove the statement using the ε, δ definition of a limit

Prove the statement using the ε, δ definition of a limit.

Q: Verify that another possible choice of δ for showing that limx→

Verify that another possible choice of δ for showing that limx→3 x2 = 9 in Example 4 is δ = min{2, ε/8}.

Q: Verify, by a geometric argument, that the largest possible choice

Verify, by a geometric argument, that the largest possible choice of δ for showing that limx→3 x2 = 9 is δ = 9 + ε - 3.

Q: Sketch the graph of an example of a function f that satisfies

Sketch the graph of an example of a function f that satisfies all of the given conditions.

Q: a. For the limit limx → 1 (x3 + x

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 t...