Infinite Limit

Calculus Level 1

$\lim_{x \rightarrow \infty} \frac{ x^3 } { 3x } - 3000 = \, ?$

As $x$ gets larger and larger, what value does this expression approach?

-3000

\infty

3000

0

1 solution

Blan Morrison
Jan 29, 2018

Since $x^3$ increases at a faster rate than $3x$ , we can say that $\displaystyle\lim_{x\rightarrow \infty}=\infty$ .

Since $\infty-n$ , where $n$ is any finite real number, is equal to $\infty$ , that means that the answer to this problem is $\boxed{\infty}$ .

@Zandra Vinegar , and @Blan Morrison , there is no proof that $\displaystyle \lim _ { x \to \infty } \frac { x ^ { 3 } } { 3x } - 3000 = \infty$ if although, the value of $x$ gets larger and larger.

. . - 3 months ago

Infinite Limit

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