Question

question
determine the limit shown below in simplest form.
(limlimits_{x \to 0} \frac{x^2 - 7x}{x^2 - 3x})

Explanation:

Step1: Factor numerator and denominator

Factor out \(x\) from numerator and denominator: \(\frac{x(x - 7)}{x(x - 3)}\)

Step2: Cancel common factor \(x\) (for \(x

eq0\))
Simplify to \(\frac{x - 7}{x - 3}\)

Step3: Substitute \(x = 0\)

Substitute \(x = 0\) into \(\frac{x - 7}{x - 3}\): \(\frac{0 - 7}{0 - 3}=\frac{-7}{-3}=\frac{7}{3}\)

Answer:

\(\frac{7}{3}\)