Question:medium

If \[ \lim_{x\to0}\frac{2^{\tan x}-2^{\sin x}}{x^2\sin x}=k, \] then \(e^{2k}=\)

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For limits involving \[ a^{u(x)}-a^{v(x)}, \] use \[ \boxed{ a^{u}-a^{v} \approx a^v\log(a)\,(u-v) } \] for small values of \[ u-v. \]
Updated On: Jul 18, 2026
  • \(1\)
  • \(\log 2\)
  • \(2\)
  • \(\dfrac12\log2\)
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The Correct Option is C

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