Answer:
-1/9
Step-by-step explanation:
[tex]\lim_{x \to 3} \frac{1/x-1/3}{x-3}[/tex]
For simplicity, let's multiply top and bottom by 3x:
[tex]\lim_{x \to 3} \frac{3-x}{3x(x-3)}[/tex]
Factor out a -1:
[tex]\lim_{x \to 3} \frac{-(x-3)}{3x(x-3)}[/tex]
Divide top and bottom by x−3:
[tex]\lim_{x \to 3} \frac{-1}{3x}[/tex]
Evaluate the limit:
[tex]\frac{-1}{3(3)}\\-\frac{1}{9}[/tex]
It's important to note that the function doesn't exist at x = 3. As x approaches 3, the function approaches -1/9.
