QuestionAugust 25, 2025

16. lim _(xarrow 3^+)(x+3)/(x-3)

16. lim _(xarrow 3^+)(x+3)/(x-3)
16. lim _(xarrow 3^+)(x+3)/(x-3)

Solution
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Answer

+\infty Explanation 1. Identify the Type of Limit As x \to 3^+, the denominator x - 3 \to 0^+ (positive from the right). 2. Analyze the Numerator The numerator x + 3 \to 6 as x \to 3^+. 3. Determine the Behavior of the Fraction Since the numerator approaches a constant (6) and the denominator approaches 0 from the positive side, \frac{6}{x-3} \to +\infty.

Explanation

1. Identify the Type of Limit<br /> As $x \to 3^+$, the denominator $x - 3 \to 0^+$ (positive from the right).<br /><br />2. Analyze the Numerator<br /> The numerator $x + 3 \to 6$ as $x \to 3^+$.<br /><br />3. Determine the Behavior of the Fraction<br /> Since the numerator approaches a constant (6) and the denominator approaches 0 from the positive side, $\frac{6}{x-3} \to +\infty$.
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