<p>If \(\lim_{x \to 1} \frac{1}{2^{x-1}}\) exists.</p>
Step-by-Step Solution
Key Concept: Evaluate the limit by direct substitution since the exponential function is continuous everywhere; as x approaches 1, the exponent (x-1) approaches 0, making 2^0 = 1.
<p><strong>Step 1:</strong> Recognize that f(x) = 1/2^(x-1) is a composition of continuous functions (exponential and reciprocal).</p><p><strong>Step 2:</strong> Since exponential functions are continuous everywhere, we can use direct substitution:</p><p>lim(x→1) 1/2^(x-1) = 1/2^(1-1) = 1/2^0 = 1/1 = 1</p><p><strong>Step 3:</strong> The limit exists and equals 1.</p><p>∴ Answer: B</p>
Correct Answer: B