# Limit of cosx/x as x approaches infinity | Lim x→∞ cosx/x

The limit of cosx/x as x approaches infinity is equal to 0. The formula of limx→∞ (cos x)/x is given below:

$\lim\limits_{x \to \infty} \dfrac{\cos x}{x}=0$.

Here we find the limit of (cos x)/x when x tends to infinity.

## Limx→∞ (cos x)/x = 0 Proof

Question: What is the limit of cosx/x when x tends to infinity?

Explanation:

The limit of cosx/x, when x→∞, will be computed using the Sandwich/Squeeze theorem of limits. We know that the value of cosx lies between -1 and 1, that is,

-1 ≤ cosx ≤ 1

For very large values of x, it follows that

$\dfrac{-1}{x} \leq \dfrac{\cos x}{x} \leq \dfrac{1}{x}$

Taking x→∞. we obtain that

limx→∞ $\dfrac{-1}{x} \leq$ limx→∞ $\dfrac{\cos x}{x} \leq$ limx→∞ $\dfrac{1}{x}$

⇒ 0 ≤ limx→∞ $\dfrac{\cos x}{x}$ ≤ 0

∴By the Sandwich theorem, the given limit

$\lim\limits_{x \to \infty} \dfrac{\cos x}{x} =0$

So the limit of cosx/x is equal to 0 when x tends to infinity, and this is proved by the Sandwich/Squeeze theorem of limits.

Read Also: Limit of sinx/x when x→∞

Limit of sinx/x when x→0

More Limits

## FAQs

### Q1: What is the limit of cosx/x when x tends to infinity?

Answer: The limit of cosx/x is equal to 0 when x tends to ∞, that is, limx→∞ cosx/x =0.