Question

Find the limit of the function algebraically.

Answer 1

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`.