Question

1. $lim_{x \to 0} \frac{x^{3}-5x^{2}}{x^{2}}$

Explanation:

Step1: Simplify the function

Divide each term in the numerator by $x^{2}$. We get $\lim_{x
ightarrow0}\frac{x^{3}}{x^{2}}-\frac{5x^{2}}{x^{2}}=\lim_{x
ightarrow0}(x - 5)$.

Step2: Evaluate the limit

Substitute $x = 0$ into $x-5$. So, $\lim_{x
ightarrow0}(x - 5)=0 - 5=-5$.

Answer:

$-5$