Question

List three conditions under which limits do not exist.
(Select all that apply.)

The limit of f(x) as x → c does not exist when f(x) approaches a different number from the right side of c than it approaches from the left side of c.

The limit of f(x) as x → c does not exist when
lim x → c f(x) = ∞/∞.

The limit of f(x) as x → c does not exist when
lim x → c f(x) = 0/0.

The limit of f(x) as x → c does not exist when f(x) oscillates between two fixed values as x approaches c.

The limit of f(x) as x → c does not exist when f(x) increases or decreases without bound as x approaches c.

Answer 1

What do you think the answer could be like narrow it down if you could

Answer 2

The limit would not exist when x -> c if:

It approaches 0/0
If f(x) approaches different numbers from the right/left.

For the third condition I'm not too certain.. but might be when it oscillates violently between two fixed values.

Answer 3

The three conditions under which limits do not exist are:

1. The limit of f(x) as x → c does not exist when f(x) approaches a different number from the right side of c than it approaches from the left side of c.

2. The limit of f(x) as x → c does not exist when lim x → c f(x) = ∞/∞.

3. The limit of f(x) as x → c does not exist when lim x → c f(x) = 0/0.

Therefore, options 1, 2, and 3 are the correct answers. Options 4 and 5 describe specific cases where the limit may not exist, but they are not general conditions under which limits do not exist.