(a) $$ \lim _{x \rightarrow 3^{+}} \frac{x-1}{x-3} $$

Question

UpStudy AI · Accepted Answer

To evaluate the limit:

$$
\lim_{x \rightarrow 3^{+}} \frac{x - 1}{x - 3}
$$

**Step 1: Analyze the Behavior as $$ x $$ Approaches 3 from the Right**

- **Numerator ($$ x - 1 $$)**:
  - As $$ x \rightarrow 3^{+} $$, $$ x - 1 $$ approaches $$ 2 $$.

- **Denominator ($$ x - 3 $$)**:
  - As $$ x \rightarrow 3^{+} $$, $$ x - 3 $$ approaches $$ 0 $$ from the positive side (since $$ x $$ is slightly greater than 3).

**Step 2: Determine the Sign of the Fraction**

- The numerator approaches a positive value ($$ 2 $$).
- The denominator approaches a small positive number ($$ 0^{+} $$).

Therefore, the entire fraction:

$$
\frac{x - 1}{x - 3} \rightarrow \frac{2}{0^{+}} = +\infty
$$

**Conclusion:**

$$
\lim_{x \rightarrow 3^{+}} \frac{x - 1}{x - 3} = +\infty
$$
The limit is positive infinity.

(a)

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Calculus Questions