Find the limit of the function algebraically.

Question

asked Jul 18, 2022 141k views

1 Answer

Harry Stuart · Answer 1 · 2022-07-24T16:14:37+0000

Given:

The given limit problem is:

$\lim_(x\to 0)(x^2+3)/(x^4)$

To find:

The value of the given limit problem.

Solution:

We have,

$\lim_(x\to 0)(x^2+3)/(x^4)$

In can be written as:

$\lim_(x\to 0)(x^2+3)/(x^4)=\lim_(x\to 0)(x^2)/(x^4)+(3)/(x^4)$

$\lim_(x\to 0)(x^2+3)/(x^4)=\lim_(x\to 0)(1)/(x^2)+(3)/(x^4)$

After applying limits, we get

$\lim_(x\to 0)(x^2+3)/(x^4)=(1)/(0^2)+(3)/(0^4)$

$\lim_(x\to 0)(x^2+3)/(x^4)=\infty+\infty$

$\lim_(x\to 0)(x^2+3)/(x^4)=\infty$

Therefore, the value of the given limit problem is
$\infty$ .