Answer :
The limit as x approaches infinity of the given function is infinity.
To apply l'Hôpital's Rule, we differentiate the numerator and the denominator separately until we no longer have an indeterminate form.
Given function:[tex]f(x) = 7x^3 + 45x^3 - 3x[/tex]
1. Take the derivative of the numerator:
[tex]f'(x) = 21x^2 + 135x^2 - 3[/tex]
2. Take the derivative of the denominator:
[tex]g'(x) = 1[/tex]
3. Apply l'Hôpital's Rule again to the new function f'(x) / g'(x):
[tex]lim (x- > ∞) f'(x) / g'(x) = lim (x- > ∞) (21x^2 + 135x^2 - 3) / 1[/tex]
4. Simplify the expression:
[tex]lim (x- > ∞) (21x^2 + 135x^2 - 3) = lim (x- > ∞) (156x^2 - 3)[/tex]
As x approaches infinity, the term with the highest power dominates. In this case, it is [tex]156x^2.[/tex]
5. Taking the limit:
[tex]lim (x- > infinity) (156x^2 - 3) = infinity[/tex]
Therefore, the limit as x approaches infinity of the given function is infinity.
Learn more about limit from the given link:
https://brainly.com/question/30679261
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