Question

\[ \lim_{n\rightarrow\infty}\frac{5n^{2}+4}{7n^{2}+6n}= \]

• A. \(0\)
• B. \(\infty\)
• C. \(\dfrac{5}{7}\)
• D. \(\dfrac{7}{5}\)

Hint:

Whenever a limit contains a rational expression in \(n\), first compare the degrees of the numerator and denominator.
• If the degrees are equal, the limit is the ratio of the leading coefficients.
• If the numerator has a smaller degree, the limit is \(0\).
• If the numerator has a larger degree, the limit is \(\infty\) (or \(-\infty\), depending on the sign). Dividing by the highest power of the variable is the quickest and most reliable method.

Answer 1

The Correct Option is C