What is the limit as x approaches infinity of a constant?

The limit of a constant as x approaches infinity is simply the constant itself. This is because a constant does not change regardless of the value of x. For example, if you have the constant value 5, as x gets larger and larger, the limit remains 5.

Understanding Limits with Constants

When we talk about limits in calculus, we often look at how functions behave as they approach a certain value. In the case of a constant:

• If f(x) = c (where c is a constant), then:
• lim (x → ∞) f(x) = c

Example for Clarity

Consider the function f(x) = 10. No matter how large x becomes, f(x) will always equal 10. Therefore:

lim (x → ∞) f(x) = 10

Key Takeaway

In summary, the limit of a constant as x approaches infinity is the constant itself, reflecting the idea that constants remain unchanged regardless of the input value.