Question

Limit as x Goes to Negative Infinity Does Not Exist

a) The limit as x goes to negative infinity can be determined solely by the function's value at negative infinity.
b) The limit as x goes to negative infinity does not exist if the function approaches different values from the left and right.
c) All functions have a defined limit as x goes to negative infinity.
d) The limit as x goes to negative infinity is always negative.

Answer 1

The limit as x goes to negative infinity does not exist if the function approaches different values from the left and right.

Step-by-step explanation:

When we say that the limit as x goes to negative infinity does not exist, it means that the function approaches different values as x approaches negative infinity from the left and right sides. In other words, the function does not have a single finite limit value.

For example, let's consider the function y = 1/x. As x approaches negative infinity, the function approaches positive infinity from the left side and negative infinity from the right side. Since the function approaches different values from the left and right, the limit as x goes to negative infinity does not exist.