Question

evaluate the limit.
limₓ→∞ 7/(4x + 3)
simplify any fractions in your answer.

Explanation:

Step1: Divide numerator and denominator by \(x\)

$$ \lim_{x ightarrow\infty}\frac{7}{4x + 3}=\lim_{x ightarrow\infty}\frac{\frac{7}{x}}{4+\frac{3}{x}} $$

Step2: Use the limit property \(\lim_{x

ightarrow\infty}\frac{c}{x}=0\) (\(c\) is a constant)
We know that \(\lim_{x
ightarrow\infty}\frac{7}{x}=0\) and \(\lim_{x
ightarrow\infty}\frac{3}{x}=0\).

$$ \lim_{x ightarrow\infty}\frac{\frac{7}{x}}{4+\frac{3}{x}}=\frac{\lim_{x ightarrow\infty}\frac{7}{x}}{\lim_{x ightarrow\infty}(4+\frac{3}{x})}=\frac{0}{4 + 0} $$

Answer:

\(0\)