Question

find the limit of the function: \\(\lim_{x \to 0} (5x(x - 9)) = \\)

Explanation:

Step1: Recall the limit law for continuous functions

For a function \( f(x) \) that is continuous at \( x = a \), \( \lim_{x \to a} f(x)=f(a) \). The function \( f(x) = 5x(x - 9) \) is a polynomial function, and all polynomial functions are continuous everywhere. So we can directly substitute \( x = 0 \) into the function.

Step2: Substitute \( x = 0 \) into the function

Substitute \( x = 0 \) into \( 5x(x - 9) \):
\[

$$\begin{align*} 5\times0\times(0 - 9)&=5\times0\times(- 9)\\ &=0 \end{align*}$$

\]

Answer:

\( 0 \)