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 limx→∞ 1/x2, so the formula of the limit of 1/x2 is given as follows:

limx→∞ 1/x2 = 0

What is the Limit of 1/x2 when x

Answer: limx→∞ $\dfrac{1}{x^2}$ = 0.

Explanation:

As limx→∞ 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

limx→∞ 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

limx 1/xn

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.

FAQs

Q1: What is limx→0 1/x2?

Answer: The limit of 1/x2 is 0 when x tends to ∞, that is, limx→∞ 1/x2 =0.

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