Limit of 1/x^2 as x approaches infinity

The limit of 1/x^2 as x approaches infinity is equal to 0. As this limit is denoted by lim_x→∞ 1/x², so the formula of the limit of 1/x² is given as follows:

lim_x→∞ 1/x² = 0

What is the Limit of 1/x² when x→∞

Answer: lim_x→∞ $\dfrac{1}{x^2}$ = 0.

Explanation:

As lim_x→∞ f(x)/g(x) is written as $\dfrac{\lim\limits_{x \to \infty}f(x)}{\lim\limits_{x \to \infty} g(x)}$, the given limit will be equal to

lim_x→∞ 1/x²

= $\dfrac{\lim\limits_{x \to \infty} 1}{\lim\limits_{x \to \infty} x^2}$

= $\dfrac{1}{\lim\limits_{x \to \infty} x^2}$

= $\dfrac{1}{\infty}$

= 0.

So the limit of 1/x² is equal to 0 when x tends to infinity.

More Limits:

Limit of xsin(1/x) when x→0

Limit of x²sin(1/x) when x→0

Limit of x^1/x when x→∞

Question-Answer

Question: Find the limit of 1/xⁿ when x→∞ (for n>1), that is find the limit

lim_x→∞ 1/xⁿ

Answer:

We will proceed as above. So the given limit can be written as limx→∞ 1/xn = $\dfrac{\lim\limits_{x \to \infty} 1}{\lim\limits_{x \to \infty} x^n}$ = $\dfrac{1}{\lim\limits_{x \to \infty} x^n}$ = 1/∞ = 0. Hence, the limit of 1 divided by xn (for n >1) is equal to 0 when x approaches infinity.

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