Limits, Continuity & Differentiability
Indeterminate forms
Grade 12
Question:
<p><strong>Ex. 40 (A):</strong> Find <span class="math">\lim_{x \to 0} \frac{\sin 2x - 2\tan x}{\ln(1 + x^3)}\</span></p>
Step-by-Step Solution
Key Concept: Apply L'Hôpital's rule or Taylor series expansion for trigonometric and logarithmic functions near zero.
<p><strong>Solution:</strong> Using L'Hôpital's rule and series expansions:</p><p>$$\lim_{x \to 0} \frac{\sin 2x - 2\tan x}{\ln(1 + x^3)} = 1$$</p><p>∴ Answer is (s)</p>
Correct Answer: s