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 lim_x→∞ (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.

Lim_x→∞ (cos x)/x = 0 Proof

Question: 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 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

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

⇒ 0 ≤ lim_x→∞ $\dfrac{\cos x}{x}$ ≤ 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

limx→0 sin(√x)/x	limx→0 sin(x2)/x
limx→0 sin3x/sin2x	limx→0 x/sinx
limx→0 tanx/x	limx→0(cosx-1)/x

FAQs