Question

evaluate the limit
lim_{x \to infty} \frac{3 + 7x}{4 - 6x}
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Explanation:

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

$$\lim_{x ightarrow\infty}\frac{\frac{3}{x}+7}{\frac{4}{x}-6}$$

Step2: Apply limit properties

As \(x
ightarrow\infty\), \(\lim_{x
ightarrow\infty}\frac{3}{x} = 0\) and \(\lim_{x
ightarrow\infty}\frac{4}{x}=0\). So we have \(\frac{0 + 7}{0-6}\)

Answer:

\(-\frac{7}{6}\)