Limits, Continuity & Differentiability
Exponential and logarithmic limits
Grade None
Question:
<p><strong>Ex. 40 (B):</strong> The value of <span class="math">\lim_{x \to 0^+} \left(x^{1/x^2} - x^{1/x}\right)\</span> equals</p>
Step-by-Step Solution
Key Concept: For exponential limits with variable exponents, convert to exponential form using logarithms.
<p><strong>Solution:</strong> Taking logarithm and analyzing the behavior:</p><p>$$\lim_{x \to 0^+} \left(x^{1/x^2} - x^{1/x}\right) = -2$$</p><p>∴ Answer is (p)</p>
Correct Answer: p