Question

evaluate the limit.
lim _ { x
ightarrow - infty } \frac { - 4 x + 7 } { 10 x + 8 }
simplify any fractions in your answer.

Explanation:

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

$$ \lim_{x\to-\infty}\frac{-4x + 7}{10x + 8}=\lim_{x\to-\infty}\frac{\frac{-4x}{x}+\frac{7}{x}}{\frac{10x}{x}+\frac{8}{x}} $$

Step2: Simplify the expression

$$ \lim_{x\to-\infty}\frac{-4+\frac{7}{x}}{10+\frac{8}{x}} $$

Step3: Use the limit property \(\lim_{x\to\pm\infty}\frac{c}{x}=0\) (\(c\) is a constant)

As \(x\to-\infty\), \(\lim_{x\to-\infty}\frac{7}{x}=0\) and \(\lim_{x\to-\infty}\frac{8}{x}=0\). So the limit becomes \(\frac{-4 + 0}{10+0}\)

Answer:

\(-\frac{2}{5}\)