Question:
Evaluate
\[
\lim_{x \to 0} \sqrt{\frac{x + 2 \sin x + 3 \tan x - \tan^3 x}{x^2 + 2 \sin x + \tan x + 3 - \sqrt{\sin^2 x - 2 \tan x - x + 3}}} = ?
\]
Evaluate
\[
\lim_{x \to 0} \sqrt{\frac{x + 2 \sin x + 3 \tan x - \tan^3 x}{x^2 + 2 \sin x + \tan x + 3 - \sqrt{\sin^2 x - 2 \tan x - x + 3}}} = ?
\]
Show Hint
Use Taylor expansions of trigonometric functions and simplify to find limits.
Updated On: Jun 6, 2025
- \(2 \sqrt{3}\)
- 10
- 25
- \(\sqrt{17}\)
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The Correct Option is A
Solution and Explanation
Use series expansions of \(\sin x\) and \(\tan x\) near zero and simplify numerator and denominator to find the limit.
The limit evaluates to \(2 \sqrt{3}\).
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