The limit of cos(1/x) as x approaches 0 does not exist. In this post, we will learn how to find the limit of cos(1/x).

lim_{x→0} cos(1/x) Does Not Exist.

## Limit of cos(1/x) when x→0

**Question:** What is the limit cos(1/x) when x tend to 0?

*Answer:* The limit of cos(1/x) does not exist when x tends to 0.

**Explanation:**

The following theorem will be used to find the limit of cos(1/x) when x tends to 0.

Theorem: If lim_{x→c} f(x) = L, then for every sequence x_{n}→c we always have lim_{n→∞} f(x_{n}) = L. |

Let

x_{n} = $\dfrac{1}{2n \pi}$

y_{n} = $\dfrac{1}{(2n+1) \pi}$.

Note that when n tends to ∞, the above two sequences

x_{n}, y_{n} →0.

But,

lim_{n→∞} f(x_{n}) = lim_{n→∞} cos 2nπ = 1.

lim_{n→∞} f(y_{n}) = lim_{n→∞} cos (2n+1)π = -1.

So by the above theorem, we conclude that the limit of cos(1/x) when x tends to 0 does not exist.

**Also Read:** Limit of sin(1/x) as x approaches 0

Limit of sinx/x when x→∞ | Limit of (cosx-1)/x when x→0

Limit of sin(x^{2})/x when x→0 | Limit of sin(√x)/x when x→0

Limit of log(1+x)/x when x→0 | Limit of (e^{x}-1)/x when x→0

Limit of (1+$\frac{1}{n})^{n} when n**→**∞

## FAQs

### Q1: What is the limit of cos(1/x) as x tends to 0?

Answer: The limit of cos(1/x) as x tends to 0 does not exit, that is, lim_{x→0} cos(1/x) = Not Exist.