Evaluate:
![\[ \lim_{x \to 0} \frac{25 x^3 + 2}{75x^7 - 2}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-e2a77eb49d301826de64957de8fcbb00_l3.png "Rendered by QuickLaTeX.com")
Since polynomials are continuous, we know the numerator and denominator are continuous. Thus,
is continuous and we can evaluate:
![\[ \lim_{x \to 0} \frac{25 x^3 + 2}{75x^7 - 2} = \frac{2}{-2} = -1. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-cc56dd3aa6c9ece3a0a303d47ae6fd23_l3.png "Rendered by QuickLaTeX.com")
Evaluate the limit
Since polynomials are continuous, we know the numerator and denominator are continuous. Thus,
is continuous and we can evaluate: