Since the grade of the numerator and the denominator is the same, then the limit exists and is distinct from 0. The limit of the expression is 4/7.
How to determine the limit of a rational expression when x tends to infinite
In this problem we must apply some algebraic handling and some known limits to determine whether the limit exists or not. The limit exists if and only if the result exists.
[tex]\lim_{x \to \infty} \frac{4\cdot x - 1}{7\cdot x + 3}[/tex]
[tex]\lim_{x \to \infty} \frac{4\cdot x - 1}{7\cdot x + 3} \cdot \frac{x}{x}[/tex]
[tex]\lim_{x \to \infty} \frac{4 - \frac{1}{x} }{7 + \frac{3}{x} }[/tex]
[tex]\lim_{x \to \infty} \frac{4}{7}[/tex]
4/7
Since the grade of the numerator and the denominator is the same, then the limit exists and is distinct from 0. The limit of the expression is 4/7.
To learn more on limits: https://brainly.com/question/12207558
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