Given:
The given limit problem is:
[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}[/tex]
To find:
The value of the given limit problem.
Solution:
We have,
[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}[/tex]
In can be written as:
[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\lim_{x\to 0}\dfrac{x^2}{x^4}+\dfrac{3}{x^4}[/tex]
[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\lim_{x\to 0}\dfrac{1}{x^2}+\dfrac{3}{x^4}[/tex]
After applying limits, we get
[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\dfrac{1}{0^2}+\dfrac{3}{0^4}[/tex]
[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\infty+\infty[/tex]
[tex]\lim_{x\to 0}\dfrac{x^2+3}{x^4}=\infty[/tex]
Therefore, the value of the given limit problem is [tex]\infty[/tex].
