Answer:
[tex]\lim_{x \to 12} \frac{\frac{1}{x}-\frac{1}{12} }{x-12} =\frac{-1}{144}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\lim_{x \to 12} \frac{\frac{1}{x}-\frac{1}{12} }{x-12}[/tex]
Step 2: Solve
- Numerator; Common denominator: [tex]\lim_{x \to 12} \frac{\frac{12}{12x}-\frac{x}{12x} }{x-12}[/tex]
- Numerator; Combine like terms: [tex]\lim_{x \to 12} \frac{\frac{12-x}{12x} }{x-12}[/tex]
- Rewrite entire fraction: [tex]\lim_{x \to 12} \frac{12-x}{12x} \div x-12[/tex]
- Rewrite operation: [tex]\lim_{x \to 12} \frac{12-x}{12x} \cdot \frac{1}{x-12}[/tex]
- Multiply: [tex]\lim_{x \to 12} \frac{12-x}{12x(x-12)}[/tex]
- Factor numerator: [tex]\lim_{x \to 12} \frac{-(x - 12)}{12x(x-12)}[/tex]
- Simplify: [tex]\lim_{x \to 12} \frac{-1}{12x}[/tex]
- Evaluate limit: [tex]\frac{-1}{12(12)} =\frac{-1}{144}[/tex]
